Warning, the protected name Chi has been redefined and unprotected There all together, 29, different equivalence classes For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 3, 4, 2]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [3, 1, 2, 4]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [2, 4, 3, 1], [4, 3, 2, 1]}} the member , {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 3, 4, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3], [2, 0], [0, 4]}, {}], [[2, 1], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}], [[1, 1], {[1, 3, 0], [0, 4, 0], [1, 2, 1], [0, 3, 1], [1, 1, 2], [0, 2, 2], [1, 0, 3], [0, 1, 3], [0, 0, 4], [2, 0, 0]}, {1, 2}], [[1, 2], {[0, 3, 0], [1, 2, 0], [1, 1, 2], [0, 1, 3], [2, 1, 0], [0, 2, 1]}, {}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[1, 2, 2], {[0, 3, 0, 0], [1, 2, 0, 0], [2, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1], [1, 1, 2, 0], [0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 1], [0, 1, 1, 2], [0, 1, 0, 3], [1, 1, 0, 2]}, {2, 3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 1, 1], [2, 1, 1, 0], [1, 1, 2, 0], [0, 1, 3, 0]}, {}] , [[1, 2, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2}], [[1, 2, 3, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [2, 3, 4, 1], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[1, 2, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 3, 0, 0], [2, 1, 1, 0, 0], [1, 1, 2, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], { [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}], [[1, 3, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 2, 0, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 1, 3, 2]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 4, 2, 3], [4, 1, 2, 3]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 1, 4], [3, 2, 4, 1]}} the member , {[1, 2, 3], [2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 1], [0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 1, 2], [0, 0, 3], [1, 1, 0], [1, 0, 1]}, {1, 2}] , [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 1, 1]}, {2}], [[2, 1], {[0, 3, 0], [1, 2, 0], [0, 1, 1]}, {}], [ [2, 1, 1], {[0, 0, 3, 0], [1, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3} ], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[0, 3, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[3, 2, 1], {[0, 1, 2, 0], [0, 1, 1, 1], [1, 2, 1, 0], [0, 3, 1, 0]}, {}], [[3, 2, 1, 1], {[1, 0, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[4, 3, 2, 1], { [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 2, 1, 0]}, {1, 2}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 20, 20, 20, 20] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [3, 4, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [2, 1, 3, 4], [4, 3, 2, 1]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 3, 1, 2]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [3, 4, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 1], [0, 3]}, {}], [[1, 1], {[0, 3, 0], [2, 1, 0], [2, 0, 1], [0, 2, 1], [0, 1, 2], [0, 0, 3]}, {1, 2}] , [[1, 2], {[2, 1, 0], [0, 1, 2], [0, 2, 0]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [ [1, 2, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 2, 2], {[2, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [2, 1, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[2, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [2, 3, 4, 1], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[3, 2, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 2, 1, 1, 1] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 1, 4, 3]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 1, 4, 3]}} the member , {[2, 3, 1], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 1, 4, 3]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[1, 2], [2, 0]}, {}], [[1, 1], {[1, 2, 0], [1, 0, 2], [2, 0, 0], [1, 1, 1]}, {1, 2}], [[1, 2], {[0, 3, 0], [0, 2, 2], [1, 1, 0]}, {1}], [[2, 1], {[0, 1, 2], [1, 1, 0], [0, 2, 0]}, {2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 15, 15, 15, 15, 15, 15, 15] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 84, 84, 84, 84] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}} the member , {[1, 3, 2], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[4, 0], [1, 2], [0, 3], [3, 1]}, {}], [[1, 1], { [0, 3, 0], [4, 0, 0], [3, 1, 0], [3, 0, 1], [1, 2, 0], [0, 2, 1], [1, 0, 2], [0, 1, 2], [0, 0, 3], [1, 1, 1]}, {1, 2}], [[1, 2], {[0, 1, 2], [1, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[0, 4, 0], [0, 3, 1], [0, 1, 2], [1, 1, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0]}, {1, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 4, 0], [0, 0, 3, 1], [0, 0, 1, 2]}, {2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2]}, {}] , [[1, 2, 3, 3], %1, {3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %1, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[4, 1, 2, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], %1, {1}], [ [3, 1, 2, 2], {[0, 1, 0, 3, 0], [0, 1, 0, 2, 1], [0, 1, 0, 1, 2], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}]] %1 := {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 2, 0, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 3, 1, 4]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [1, 4, 2, 3]}} the member , {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 2], {[2, 1, 0], [0, 2, 0], [0, 1, 1]}, {1}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[2, 1], {[0, 1, 2], [0, 2, 0]}, {}], [[2, 1, 1], {[0, 0, 1, 2], [0, 1, 1, 0], [0, 0, 2, 0]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 2], {[2, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 2]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 2]}, {3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[3, 2, 1, 4], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 2], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {}], [[3, 2, 1, 5, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], { [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 2]}, {4, 5}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {1}], [ [5, 4, 3, 2, 1], {[0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {2, 3, 4}], [[5, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], { [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 1, 1], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[5, 4, 3, 1, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 4, 4, 4, 4] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [1, 2, 4, 3]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 1], [3, 0]}, {}], [[1, 1], {[3, 0, 0], [2, 1, 0], [2, 0, 1]}, {1, 2}], [[1, 2], {[2, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[2, 1, 0], [0, 2, 0], [0, 1, 1]}, {}], [ [1, 2, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 2, 2], {[2, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [2, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [ [2, 1, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {2, 3} ], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[2, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 1], %1, {1}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [2, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0], [0, 1, 2, 1, 0]}, {2, 3}], [[2, 3, 4, 1], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %1, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], %1, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]] %1 := {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 4, 4, 4, 4] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 3, 2, 1]}} the member , {[1, 3, 2], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 0], [0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 1, 2], [0, 0, 3], [2, 0, 0]}, {1, 2}], [[2, 1], {[0, 1, 3], [1, 1, 0], [0, 2, 0]}, {}], [[1, 2], {[2, 1, 0], [0, 1, 2], [0, 2, 0]}, {}], [[1, 2, 2], {[2, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {2}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 2]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 3], [0, 0, 2, 0]}, {2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 2]}, {}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 2]}, {2, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 0, 2], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 2]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], { [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 0, 2], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {2, 4}], [[2, 3, 1, 4], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], {[0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[2, 1, 3, 4, 5], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[2, 3, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 5, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 6, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 20, 0, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2], [3, 1], [5, 0]}, {}], [[1, 1], {[3, 1, 0], [3, 0, 1], [5, 0, 0], [0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}] , [[2, 1], {[0, 3, 0], [3, 1, 0], [0, 1, 1]}, {}], [[1, 2], {[3, 1, 0], [0, 2, 0], [0, 1, 1]}, {}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3} ], [[2, 3, 1], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [ [2, 1, 1], {[0, 0, 3, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3} ], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 2, 1], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 1, 2, 2], { [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1, 2, 4}], [[4, 2, 3, 1], {[1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 3, 1, 1, 0], [0, 1, 2, 1, 0]}, {}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4} ], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 4, 1, 2, 2], %2, {4, 5}], [[3, 4, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], { [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 1, 1], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3}], [[4, 2, 3, 1, 2], %2, {2}], [[5, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [ [4, 2, 3, 1, 1], {[1, 0, 1, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 2, 3, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 8, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 23, 1, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [3, 4, 2, 1]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [2, 1, 3, 4], [4, 1, 2, 3]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 3, 4, 1]}} the member , {[1, 2, 3], [2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [3, 4, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 1], [0, 3]}, {}], [[1, 1], {[0, 3, 0], [2, 1, 0], [2, 0, 1], [0, 2, 1], [0, 1, 2], [0, 0, 3]}, {1, 2}] , [[1, 2], {[0, 3, 0], [2, 1, 0], [0, 1, 1]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [ [1, 2, 2], {[0, 3, 0, 0], [2, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [ [1, 2, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [2, 1, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[2, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2, 2], {[2, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 3, 1], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [2, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[3, 2, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 3, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 4, 1, 1, 1] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [1, 3, 2, 4]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]}} the member , {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [1, 3, 2, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 0]}, {}], [[1, 1], {[2, 0, 0]}, {1, 2}], [[1, 2], {[0, 3, 0], [0, 2, 1], [1, 1, 0]}, {}], [[2, 1], {[1, 1, 0], [0, 2, 0]}, {}], [ [1, 2, 2], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1], [1, 1, 0, 0]}, {2, 3} ], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 0]}, {3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 0]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1}], [[2, 1, 3], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 3, 0], [0, 1, 2, 1]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 3, 0, 0], [0, 1, 2, 1, 0], [0, 1, 2, 0, 1], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {1, 2}], [[2, 1, 4, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 11, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 39, 20, 20, 20] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}} the member , {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [2, 1], [0, 2]}, {}], [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}], [[1, 1], {[4, 0, 0], [2, 1, 0], [2, 0, 1], [0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}] , [[2, 1], {[0, 3, 0], [2, 2, 0], [3, 1, 0], [0, 2, 1], [0, 1, 2], [1, 1, 1]}, {}], [ [2, 1, 1], {[0, 0, 3, 0], [1, 0, 1, 1], [0, 0, 2, 1], [3, 0, 1, 0], [2, 0, 2, 0], [0, 0, 1, 2], [0, 1, 1, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0]}, {}] , [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4} ], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1}], [[4, 3, 1, 2], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [ [4, 3, 1, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 2, 0, 0, 0] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 3, 2, 4]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 2, 3, 1], [4, 3, 2, 1]}} the member , {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 3, 2, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 0], [0, 4]}, {}], [[1, 1], {[0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [2, 0, 0]}, {1, 2}] , [[1, 2], {[0, 3, 0], [0, 1, 3], [0, 2, 1], [1, 1, 0]}, {}], [[2, 1], {[0, 1, 4], [1, 1, 0], [0, 2, 0]}, {}], [[1, 2, 2], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [0, 1, 0, 3], [1, 1, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3], [0, 0, 2, 0]}, {3} ], [[1, 2, 3], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 3, 0]}, {}], [[2, 1, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [0, 1, 0, 3], [1, 1, 0, 0], [0, 2, 0, 0]}, {1}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 2], [0, 0, 1, 4], [0, 0, 2, 0]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 3]}, {}] , [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 3, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [ [1, 2, 4, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0], [0, 1, 2, 1, 0]}, {1, 2}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 1, 1, 2], [0, 1, 1, 0, 3], [0, 1, 1, 3, 0], [0, 2, 1, 0, 0], [0, 1, 1, 2, 1], [0, 1, 3, 0, 0], [0, 1, 2, 1, 0], [0, 1, 2, 0, 1], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[1, 2, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], { [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}], [[1, 3, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 11, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 39, 1, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 1, 2], [2, 3, 4, 1], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [1, 4, 3, 2]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [4, 1, 2, 3], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [3, 1, 2], [2, 3, 4, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2], [3, 0]}, {}], [[1, 1], {[3, 0, 0], [1, 2, 0], [1, 0, 2], [1, 1, 1]}, {1, 2}], [[1, 2], {[3, 1, 0], [0, 2, 0], [1, 1, 1]}, {}], [[2, 1], {[2, 1, 0], [0, 2, 0], [0, 1, 1]}, {}], [ [1, 2, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3} ], [ [1, 2, 2], {[1, 1, 1, 0], [1, 1, 0, 1], [3, 1, 0, 0], [0, 2, 0, 0]}, {2, 3} ], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [2, 1, 1, 0]}, {}], [ [2, 1, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {2, 3} ], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[2, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [2, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 2, 1, 1, 1] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [3, 2, 1], [2, 3, 4, 1], [4, 1, 2, 3]}} the member , {[1, 2, 3], [2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1], [0, 3]}, {}], [[1, 1], {[0, 3, 0], [2, 1, 0], [2, 0, 1], [0, 2, 1], [0, 1, 2], [0, 0, 3]}, {1, 2}] , [[2, 1], {[0, 1, 3], [0, 2, 0], [1, 1, 1]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 2, 3}], [ [1, 2, 2], {[0, 3, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 1], {[0, 2, 1, 0], [1, 1, 1, 0], [1, 0, 1, 1], [0, 1, 1, 1], [0, 0, 1, 3], [0, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 3, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 3, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[2, 1, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {}], [[2, 1, 4, 3, 2], %3, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %5, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], %4, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %5, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}], [[2, 1, 4, 3, 4], %1, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %5, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %5, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], { [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[4, 3, 2, 1, 2], %3, {1, 2, 3, 4, 5}], [[5, 4, 2, 1, 3], %5, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %5, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 1, 1], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 1, 3], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 1, 2], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], { [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0]}, {4, 5}], [[2, 4, 3, 2, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 2, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0], [0, 2, 0, 0, 1, 0]}, {4, 5}], [[3, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], { [0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 2, 1, 0, 0, 0]}, {4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 1, 0, 1, 1, 0]} %4 := {[0, 0, 1, 1, 1, 0]} %5 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 6, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 9, 2, 1, 1, 1] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [3, 1, 2], [2, 1, 3, 4], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [3, 1, 2], [2, 3, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [1, 4, 3, 2]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [4, 1, 2, 3], [4, 3, 1, 2]}} the member , {[1, 3, 2], [2, 3, 1], [3, 1, 2], [2, 1, 3, 4], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2], [2, 1]}, {}], [[1, 1], {[1, 2, 0], [2, 1, 0], [2, 0, 1], [1, 0, 2], [1, 1, 1]}, {1, 2}], [[2, 1], {[0, 1, 2], [0, 2, 0], [1, 1, 1]}, {}], [[1, 2], {[1, 1, 0], [0, 2, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 1, 1], { [0, 2, 1, 0], [1, 1, 1, 0], [1, 0, 1, 1], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1}], [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[5, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], { [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 1, 1], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 2, 2, 2, 2] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 3, 2, 1]}, {[1, 3, 2], [2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 1], [0, 3], [5, 0]}, {}], [[1, 1], { [0, 3, 0], [5, 0, 0], [0, 2, 1], [0, 1, 2], [0, 0, 3], [1, 1, 0], [1, 0, 1] }, {1, 2}], [[1, 2], {[0, 1, 2], [1, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[0, 4, 0], [1, 2, 0], [4, 1, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 3, 0]}, {1}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 2, 0], [4, 0, 1, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 4, 1, 0]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 4}], [[3, 2, 1, 1], {[0, 0, 4, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 3, 1, 0]}, {}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], { [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {1, 2}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], {[0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 1, 1], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 3, 1, 0]}, {4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 3, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 4, 1, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [3, 4, 1, 2]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [2, 1, 4, 3], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [2, 1], [0, 3]}, {}], [[1, 1], { [0, 3, 0], [4, 0, 0], [2, 1, 0], [2, 0, 1], [0, 2, 1], [0, 1, 2], [0, 0, 3] }, {1, 2}], [[1, 2], {[2, 1, 0], [0, 1, 2], [0, 2, 0]}, {}], [[2, 1], {[0, 4, 0], [1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 2, 3}], [ [1, 2, 2], {[2, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [2, 1, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[1, 0, 1, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 3, 0]}, {}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[2, 3, 4, 1], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 1, 2, 2], {[0, 1, 0, 3, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], %5, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], %5, {1, 2, 3, 4, 5}], [[1, 3, 4, 1, 2], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0]}, {4, 5}], [[2, 3, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 5, 2, 1], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], { [1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[2, 3, 5, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 5], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], %5, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], { [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], {[1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0], [0, 2, 0, 0, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], { [0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 2, 1, 0, 0, 0]}, {4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 1, 0, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[0, 0, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 6, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 9, 2, 0, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 2, 1], [3, 4, 1, 2], [4, 1, 2, 3]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [2, 1, 4, 3], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [3, 2, 1], [2, 3, 4, 1], [3, 4, 1, 2]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [2, 1, 4, 3]}} the member , {[1, 3, 2], [2, 1, 3], [3, 2, 1], [3, 4, 1, 2], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1], [3, 0]}, {}], [[1, 1], {[3, 0, 0], [2, 1, 0], [2, 0, 1]}, {1, 2}], [[1, 2], {[2, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[1, 2, 2], {[2, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [2, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[1, 0, 1, 0], [0, 0, 3, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [2, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0], [0, 1, 2, 1, 0]}, {2, 3}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 1, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 1, 2], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0]}, {4, 5}], [[2, 3, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 5, 2, 1], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], { [1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[2, 3, 5, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %4, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], {[1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0], [0, 2, 0, 0, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], { [0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 2, 1, 0, 0, 0]}, {4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 1, 0, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 6, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 9, 4, 4, 4, 4] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 3, 4, 1]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [4, 1, 2, 3]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 3, 1, 2]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 1, 4], [3, 4, 2, 1]}} the member , {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3], [2, 0]}, {}], [[2, 1], {[0, 1, 2], [1, 1, 0], [0, 2, 0]}, {1}], [[1, 1], {[1, 3, 0], [1, 2, 1], [1, 1, 2], [1, 0, 3], [2, 0, 0]}, {1, 2}], [[1, 2], {[1, 1, 2], [2, 1, 0], [0, 2, 0]}, {}], [[1, 2, 2], {[2, 1, 0, 0], [1, 1, 2, 0], [1, 1, 1, 1], [1, 1, 0, 2], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 2]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 2]}, {1}], [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 2]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[2, 3, 1, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[2, 3, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 5, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 3, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 4, 1, 1, 1] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 2], [0, 3]}, {}], [[1, 1], { [0, 3, 0], [1, 2, 0], [0, 2, 1], [1, 0, 2], [0, 1, 2], [0, 0, 3], [1, 1, 1] }, {1, 2}], [[1, 2], {[0, 1, 2], [0, 2, 0], [1, 1, 1]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3}], [ [1, 2, 2], {[0, 1, 2, 0], [1, 1, 1, 0], [1, 1, 0, 1], [0, 1, 1, 1], [0, 1, 0, 2], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[3, 2, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 20, 20, 20, 20] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [3, 2, 1], [2, 1, 3, 4], [3, 1, 2, 4]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [2, 4, 3, 1], [3, 4, 2, 1]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [1, 3, 4, 2]}} the member , {[1, 3, 2], [2, 3, 1], [3, 2, 1], [2, 1, 3, 4], [3, 1, 2, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 2], [2, 1]}, {}], [[1, 1], {[1, 2, 0], [2, 1, 0], [2, 0, 1], [1, 0, 2], [1, 1, 1]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[0, 2, 1], [0, 1, 2], [1, 1, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 1, 1], { [1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 1, 2]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {[0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2, 3}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 4, 4, 4, 4] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [2, 4, 3, 1]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 3, 4, 2], [2, 3, 4, 1]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [3, 1, 2, 4], [4, 1, 2, 3]}} the member , {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1], [0, 2]}, {}], [[1, 1], {[2, 1, 0], [2, 0, 1], [0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}], [[2, 1], {[0, 3, 0], [1, 2, 0], [0, 2, 1], [0, 1, 2], [1, 1, 1]}, {}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 3, 0], [1, 0, 2, 0], [1, 0, 1, 1], [0, 0, 2, 1], [0, 0, 1, 2], [0, 1, 1, 0]}, {2, 3}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[3, 2, 1], {[0, 1, 2, 0], [0, 1, 1, 1], [1, 2, 1, 0], [0, 3, 1, 0]}, {}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[1, 0, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 1, 2], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1}], [[4, 3, 2, 1], { [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 2, 1, 0]}, {}], [[5, 3, 2, 1, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], {[0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3}], [[5, 4, 2, 1, 3], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], {[0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 1, 1], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3}], [ [4, 3, 2, 1, 1], {[0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1], [1, 0, 2, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 3, 2, 1, 2], {[1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {1, 2, 3, 5}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 2, 2, 2, 2, 2, 2] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 20, 20, 20, 20] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 1, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3], [2, 0]}, {}], [[1, 1], {[1, 3, 0], [1, 2, 1], [1, 1, 2], [1, 0, 3], [2, 0, 0]}, {1, 2}], [[2, 1], {[0, 1, 3], [1, 1, 0], [0, 2, 0]}, {}], [[1, 2], {[0, 3, 0], [0, 2, 2], [1, 1, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0]}, {1, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 3, 0, 0], [0, 2, 2, 0], [0, 2, 1, 1], [0, 2, 0, 2], [1, 1, 0, 0]}, {2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 2]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [1, 1, 0, 0], [0, 2, 0, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 3], [0, 0, 2, 0]}, {2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 3, 0]}, {}], [[1, 2, 3, 2], {[0, 1, 1, 1, 1], [0, 1, 0, 2, 0], [0, 1, 0, 1, 2], [0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [1, 1, 0, 1, 0]}, {2, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 1, 1, 1, 1], [0, 1, 0, 2, 0], [0, 1, 0, 1, 2], [0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], { [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 0, 2], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {2, 4}], [[1, 3, 2, 4], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 3, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[2, 1, 4, 3], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 4], { [0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[1, 4, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}], [[2, 1, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 7, 1, 1, 1, 1, 1, 1] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 21, 1, 1, 1] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [1, 4, 2, 3]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 1, 4]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 4, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [1, 1], [0, 4]}, {}], [[1, 1], {[4, 0, 0], [0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [1, 1, 0], [1, 0, 1] }, {1, 2}], [[1, 2], {[0, 4, 0], [1, 1, 0], [0, 1, 1]}, {}], [[2, 1], {[0, 3, 0], [3, 1, 0], [1, 2, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 0, 3, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 3, 2], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[0, 3, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[0, 0, 3, 0], [1, 0, 2, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {1}], [[1, 3, 2, 2], {[0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 4, 3, 2], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4} ], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 3, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 4, 0, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 1, 4, 3]}} the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [0, 2], [3, 1]}, {}], [[1, 1], {[4, 0, 0], [3, 1, 0], [3, 0, 1], [0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}] , [[1, 2], {[3, 1, 0], [0, 2, 0], [0, 1, 1]}, {}], [[2, 1], {[0, 3, 0], [2, 2, 0], [3, 1, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 2, 3}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [2, 1, 1, 0]}, {}], [[2, 1, 1], {[0, 0, 3, 0], [3, 0, 1, 0], [2, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[2, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 2, 1], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [2, 1, 1, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [2, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 2, 1], %3, {}], [[2, 3, 1, 2], { [2, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [2, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1, 2, 4}], [[4, 2, 3, 1], %3, {}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4} ], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], %3, {}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], { [1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[3, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], {[1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[5, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], { [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {2}], [[5, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[5, 4, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], { [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0], [2, 1, 0, 0, 1, 0], [0, 2, 0, 0, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 1], { [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 1, 0, 1, 1], [0, 1, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], {[0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {4}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 5, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 7, 0, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[1, 3, 2], [2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}} the member , {[1, 2, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1], [3, 0], [0, 4]}, {}], [[1, 1], {[3, 0, 0], [0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [2, 1, 0], [2, 0, 1] }, {1, 2}], [[2, 1], {[0, 1, 4], [2, 1, 0], [0, 2, 0], [1, 1, 1]}, {}], [[1, 2], {[0, 4, 0], [1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 3, 2], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [[2, 1, 1], {[2, 0, 1, 0], [0, 2, 1, 0], [1, 1, 1, 0], [1, 0, 1, 1], [0, 1, 1, 2], [0, 0, 1, 4], [0, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[1, 4, 3, 2], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 3, 1, 0]}, {2}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [2, 1, 3, 3], {[0, 1, 4, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[2, 1, 3, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {}], [[1, 5, 4, 3, 2], %4, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], %3, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %4, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %4, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %4, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[1, 5, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], { [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0]}, {4, 5}], [[2, 4, 3, 2, 1], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], {[1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0], [0, 2, 0, 0, 1, 0]}, {4, 5}], [[3, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], { [0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 2, 1, 0, 0, 0]}, {4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 0, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 6, 3, 1, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 9, 4, 1, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [1, 1], [0, 4]}, {}], [[1, 1], {[4, 0, 0], [0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [1, 1, 0], [1, 0, 1] }, {1, 2}], [[2, 1], {[0, 4, 0], [1, 2, 0], [2, 1, 0], [0, 1, 1]}, {}], [[1, 2], {[0, 4, 0], [1, 1, 0], [0, 1, 1]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [ [1, 2, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 3, 2], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[2, 0, 1, 0], [1, 0, 2, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [ [2, 1, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 1, 2], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 3, 1, 0]}, {}], [[1, 3, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1, 2, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 4, 3, 2], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1, 2, 4}], [[4, 1, 3, 2], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[5, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 6, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 20, 0, 0, 0] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [2, 1, 4, 3]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 2, 3, 1]}} the member , {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [2, 1, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 0]}, {}], [[1, 1], {[2, 0, 0]}, {1, 2}], [[1, 2], {[0, 3, 0], [0, 2, 1], [1, 1, 0]}, {}], [[2, 1], {[1, 1, 0], [0, 2, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 0]}, {1}], [ [1, 2, 2], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1], [1, 1, 0, 0]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 3], {[0, 2, 1, 0], [1, 1, 1, 0], [0, 1, 3, 0], [0, 1, 2, 1]}, {}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 3, 0, 0], [0, 1, 2, 1, 0], [0, 1, 2, 0, 1], [1, 1, 1, 0, 0]}, {3, 4}], [[1, 2, 4, 3], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1], [0, 1, 2, 1, 0]}, {1, 2}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], { [0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 3, 0], [0, 1, 1, 2, 1], [0, 1, 2, 1, 0]}, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 1, 0, 2, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[2, 1, 3, 4], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 0]}, {}], [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], {[0, 2, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0]}, {4, 5}], [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {3, 4}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 11, 11, 11, 11, 11, 11, 11] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 39, 39, 39, 39] Out of a total of , 29, cases 29, were successful and , 0, failed Success Rate: , 1. Here are the failures {}