Warning, the protected name Chi has been redefined and unprotected There all together, 20, different equivalence classes For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 4, 3]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [2, 1, 3, 4]}, {[1, 3, 2], [2, 1, 3], [3, 1, 2], [3, 4, 2, 1]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [4, 3, 1, 2]}} the member , {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 1]}, {}], [[1, 1], {[1, 1, 0], [1, 0, 1]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2], {[1, 1, 0], [0, 2, 1]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [ [1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[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], {[1, 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, 1]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], { [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 4}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {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, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[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}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[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, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 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, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 4, 4, 4, 4, 4, 4, 4] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 5, 5, 5, 5] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 4, 2, 3]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 4, 1]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 3, 1, 4]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 1, 3, 2]}} the member , {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 4, 2, 3]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 1]}, {}], [[1, 1], {[1, 1, 0], [1, 0, 1]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 1, 1]}, {}], [[1, 2], {[1, 1, 0], [0, 3, 0], [0, 2, 1]}, {}], [ [1, 2, 2], {[1, 1, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3} ], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 0, 3, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 3} ], [[1, 2, 3], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 2, 1, 0], [1, 1, 1, 0, 0], [0, 1, 3, 0, 0], [0, 1, 2, 0, 1]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 2, 1], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {1, 2}], [[3, 1, 2, 3], { [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 3, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 1, 2, 4], {[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, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}]] 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, 10, 10, 10, 10, 10, 10, 10] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 35, 35, 35, 35] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 2, 3, 1]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 3, 2, 4]}} the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[1, 2], {[0, 2, 0], [0, 1, 1]}, {}], [[2, 1], {[0, 1, 1], [1, 2, 0], [0, 3, 0]}, {}], [[1, 2, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[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, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [ [2, 1, 1], {[0, 0, 3, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3} ], [[3, 2, 1], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [1, 0, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 4, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 2], { [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2, 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}], [[3, 2, 1, 1], { [0, 0, 1, 2, 0], [1, 0, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[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}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 4, 4, 4, 4, 4, 4, 4] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 36, 36, 36, 36, 36, 36, 36] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 400, 400, 400, 400] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 2, 1], [1, 2, 3, 4]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [3, 2, 1], [1, 2, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3], [4, 0]}, {}], [[1, 1], {[4, 0, 0], [0, 3, 0], [0, 2, 1], [0, 1, 2], [0, 0, 3]}, {1, 2}], [[1, 2], {[4, 1, 0], [0, 2, 0], [0, 1, 2]}, {}], [[2, 1], {[0, 4, 0], [1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 2], {[4, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 4, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[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}], [ [2, 1, 1], {[0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {2, 3} ], [[3, 1, 2], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[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, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 4, 1, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 3, 1, 0], [0, 1, 1, 2, 0]}, {2}], [[2, 4, 1, 3], {[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, 3, 1, 2], { [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 1, 2, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 3, 0]}, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 2, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {}], [[4, 2, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], { [0, 2, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 1]}, {4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], %2, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], { [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}], [[4, 1, 2, 3, 5], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %2, {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, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], {[0, 2, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0], [1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1]}, {4, 5}], [[1, 3, 4, 1, 2], %1, {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, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], { [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 2, 0], [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1]}, {4, 5}]] %1 := {[0, 0, 1, 1, 1, 0]} %2 := {[0, 1, 0, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 3, 2, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 6, 5, 3, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 9, 7, 4, 1, 0] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 2, 1], [2, 3, 4, 1]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [1, 4, 3, 2]}, {[1, 3, 2], [2, 1, 3], [3, 2, 1], [4, 1, 2, 3]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1, 4]}} the member , {[1, 3, 2], [2, 1, 3], [3, 2, 1], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 2, 0], [1, 0, 2]}, {1, 2}], [[1, 2], {[0, 2, 0], [1, 1, 1]}, {}], [[2, 1], {[1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [ [1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 1], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 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], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 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, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}], [[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, 3, 1, 2], { [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 1, 2, 4], {[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, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 1, 2, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 2, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 1]}, {4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 5, 3], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], %3, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %2, {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, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], { [0, 2, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0], [1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1]}, {4, 5}], [[1, 3, 4, 1, 2], %1, {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, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], { [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 2, 0], [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1]}, {4, 5}]] %1 := {[0, 0, 1, 1, 1, 0]} %2 := {[0, 1, 0, 1, 1, 0]} %3 := {[0, 1, 1, 0, 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, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 6, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 9, 7, 7, 7, 7] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4]}} the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2], [5, 0]}, {}], [[1, 1], {[5, 0, 0], [0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[1, 2], {[0, 2, 0], [0, 1, 1]}, {}], [[2, 1], {[3, 1, 0], [0, 1, 1], [0, 3, 0]}, {}], [[1, 2, 2], {[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}], [[2, 3, 1], {[3, 1, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[3, 0, 1, 0], [0, 0, 3, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3} ], [[2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {3}], [[3, 1, 2], {[3, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1, 2], {[0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [3, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [3, 0, 1, 1, 0]}, {3, 4}], [[3, 1, 2, 2], { [0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [3, 1, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 1, 2, 3], {[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, 1], { [0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1, 2, 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}], [[4, 2, 3, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[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}], [[4, 3, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 3, 1, 1, 0]}, {4, 5}], [ [5, 3, 4, 1, 2], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0]}, {2, 3}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 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, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], { [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 1, 1, 1]}, {2}], [[5, 4, 2, 3, 1], %1, {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], %1, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %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, 2], {[0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[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, 1, 1, 0, 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, 4, 3, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 15, 5, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 48, 7, 1, 0] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 2, 1]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3], [4, 3, 1, 2]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4]}} the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2], [3, 1]}, {}], [[2, 1], {[3, 2, 0], [0, 1, 1], [0, 3, 0]}, {1}], [[1, 1], {[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]}, {}], [ [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]}, {3}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 2], { [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 2, 0], [0, 0, 3, 1, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 4, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %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, 2, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 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, 4, 4, 4, 4, 4, 4, 4] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 20, 20, 20, 20, 20, 20, 20] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 103, 103, 103, 103] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 2, 1], [3, 4, 1, 2]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2], [2, 1, 4, 3]}} the member , {[1, 3, 2], [2, 1, 3], [3, 2, 1], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[1, 1], {[2, 1, 0], [2, 0, 1]}, {1, 2}], [[1, 2], {[0, 2, 0], [2, 1, 0]}, {}], [[2, 1], {[1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0], [2, 1, 0, 0]}, {2, 3}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 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], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [2, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 4, 3], {[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, 1, 2, 1, 0], [0, 2, 1, 1, 0], [2, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[3, 4, 2, 1], {[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, 1], { [0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[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, 3, 1, 2], { [0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 1, 2, 4], {[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, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 1, 2, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {}], [[4, 2, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], { [0, 2, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 1]}, {4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 5, 2, 1], %3, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], { [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[2, 3, 5, 1, 4], %3, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %3, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %3, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %3, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %1, {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, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], { [0, 2, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0], [1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1]}, {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, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 2, 0], [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1]}, {4, 5}]] %1 := {[0, 1, 0, 1, 1, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 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, 6, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 9, 7, 7, 7, 7] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 3, 1], [4, 2, 1, 3]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 3, 4, 2]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [2, 4, 3, 1]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [3, 1, 2, 4]}} the member , {[1, 2, 3], [1, 3, 2], [2, 3, 1], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 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], {[1, 2, 0], [0, 3, 0], [0, 2, 1], [0, 1, 2]}, {}], [[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], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[0, 0, 3, 0], [0, 1, 1, 0], [1, 0, 2, 0], [0, 0, 2, 1], [0, 0, 1, 2]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 1, 2], [0, 1, 2, 0]}, {}] , [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 2, 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, 4], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 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}], [[3, 2, 1, 1], { [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [1, 0, 2, 1, 0], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 1]}, {3, 4}], [[4, 3, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[3, 2, 1, 3], { [0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1}], [[3, 2, 1, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2}], [[4, 3, 2, 1], {[0, 1, 1, 1, 2], [0, 1, 2, 1, 0], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 1, 2, 0], [0, 2, 1, 1, 1]}, {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, 8, 8, 8, 8, 8, 8, 8, 8] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 23, 23, 23, 23] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 1, 2]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1], [2, 1, 4, 3]}} the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[2, 1], {[0, 1, 1], [0, 3, 0]}, {1}], [[1, 2], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {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, 3, 1, 2], {[0, 1, 0, 1, 1], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[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}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 4, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0]}, {3, 4}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], { [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[4, 5, 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, 4, 5, 6, 7, 8, 9, 10] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 24, 33, 42, 51, 60, 69, 78] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 148, 212, 276, 340] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 1, 2], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 3, 2, 1]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4]}} the member , {[1, 2, 3], [1, 3, 2], [3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {[0, 2], [3, 0]}, {}], [[1, 2], {[3, 1, 0], [0, 2, 0], [0, 1, 1]}, {1}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2], [3, 0, 0]}, {1, 2}], [[2, 1], {[0, 2, 0], [2, 1, 0], [0, 1, 2]}, {}], [ [2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [2, 0, 1, 0], [0, 0, 1, 2]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[3, 2, 1], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {2}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 2, 3}]] 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, 15, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 84, 0, 0, 0] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1], [4, 3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [3, 4, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [2, 1, 3, 4]}} the member , {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 0]}, {}], [[1, 1], {[2, 0, 0]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}], [[1, 2], {[2, 1, 0], [1, 2, 0], [0, 3, 0]}, {}], [[1, 2, 2], {[2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {2, 3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[1, 2, 1, 0], [2, 1, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [1, 2, 1, 0, 0], [2, 1, 1, 0, 0], [0, 3, 1, 0, 0]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 3, 4, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[1, 2, 3, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2}], [[1, 2, 3, 4], { [0, 1, 2, 1, 0], [1, 2, 1, 1, 0], [2, 1, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 4, 2, 1], {[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, 1], { [0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[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}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], {[1, 2, 1, 1, 0, 0], [2, 1, 1, 1, 0, 0], [0, 3, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[1, 2, 3, 5, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 2], {[0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 1, 1, 1]}, {1, 2}], [[1, 2, 3, 4, 5], {[0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 1, 1, 0]}, {3, 4}], [ [1, 3, 4, 5, 2], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0]}, {1, 2, 3, 4}]] 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, 8, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 7, 7, 7, 7] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [1, 2, 3, 4]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [4, 3, 2, 1]}} the member , {[2, 1, 3], [3, 1, 2], [3, 2, 1], [1, 2, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 0], [1, 3], [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], {[1, 1, 2], [0, 2, 2], [0, 1, 3], [2, 1, 0], [1, 2, 0], [0, 3, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0], [1, 1, 1, 1], [0, 2, 1, 1], [0, 1, 2, 1], [1, 1, 0, 2], [0, 2, 0, 2], [0, 1, 1, 2], [0, 1, 0, 3], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {2, 3}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[1, 2, 1, 0], [2, 1, 1, 0], [0, 3, 1, 0], [1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0], [0, 1, 1, 1]}, {}], [[2, 3, 4, 1], %2, {1, 2, 3}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 1, 1, 0, 1], [1, 2, 1, 0, 0], [2, 1, 1, 0, 0], [0, 3, 1, 0, 0], [1, 1, 2, 0, 0], [0, 2, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 3, 0, 0]}, {3, 4} ], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 3, 4, 2], %2, {1}], [ [1, 2, 3, 2], {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]}, {1, 2}], [[1, 2, 4, 3], %2, {}], [[3, 4, 2, 1], {[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, 1], { [0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[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, 3, 5, 4, 1], %1, {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, 1], {[0, 0, 1, 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, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], { [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 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 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 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, 8, 3, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 3, 0, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 4, 2, 1]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1], [4, 3, 1, 2]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1], [1, 2, 4, 3]}} the member , {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 1, 3, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 0]}, {}], [[1, 1], {[2, 0, 0]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 2, 0], [0, 1, 2]}, {1}], [[1, 2], {[0, 2, 0], [2, 1, 0]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2], [1, 0, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0], [2, 1, 0, 0]}, {2, 3}], [[1, 2, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 1], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], { [0, 1, 1, 1, 2], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [2, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 4, 3], {[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, 1, 2, 1, 0], [0, 2, 1, 1, 0], [2, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}], [[1, 2, 3, 1], {[0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[3, 4, 2, 1], {[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, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {1, 2, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[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, 3, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 10, 10, 10, 10, 10, 10, 10] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 84, 35, 35, 35, 35] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 2, 1, 4]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1], [4, 1, 2, 3]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2], [1, 4, 3, 2]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1], [2, 3, 4, 1]}} the member , {[1, 2, 3], [1, 3, 2], [2, 3, 1], [3, 2, 1, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 1], [0, 2]}, {}], [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}], [[1, 1], {[0, 2, 0], [2, 1, 0], [0, 1, 1], [0, 0, 2], [2, 0, 1]}, {1, 2}], [[2, 1], {[2, 2, 0], [1, 1, 1], [0, 3, 0], [0, 2, 1], [0, 1, 2]}, {}], [ [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], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[3, 2, 1], {[2, 2, 1, 0], [0, 3, 1, 0], [1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[2, 0, 2, 0], [0, 0, 3, 0], [0, 1, 1, 0], [1, 0, 1, 1], [0, 0, 2, 1], [0, 0, 1, 2]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 2, 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, 4], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 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}]] 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, 8, 8, 8, 8, 8, 8, 8, 8] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 23, 23, 23, 23] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [2, 3, 1], [1, 2, 3, 4]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [4, 3, 2, 1]}, {[1, 3, 2], [2, 1, 3], [3, 1, 2], [1, 2, 3, 4]}} the member , {[1, 3, 2], [2, 1, 3], [2, 3, 1], [1, 2, 3, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 1], [0, 3]}, {}], [[1, 1], {[1, 1, 0], [1, 0, 1], [0, 3, 0], [0, 2, 1], [0, 1, 2], [0, 0, 3]}, {1, 2}] , [[2, 1], {[0, 4, 0], [0, 1, 1], [1, 2, 0]}, {1}], [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 2]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0]}, {3, 4}]] 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, 8, 8, 8, 8, 8, 8, 8, 8] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 23, 23, 23, 23] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 1, 2], [2, 3, 4, 1]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [4, 1, 2, 3]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 4, 3, 2]}} the member , {[1, 3, 2], [2, 1, 3], [3, 1, 2], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 2, 0], [1, 0, 2]}, {1, 2}], [[1, 2], {[0, 2, 0], [1, 1, 1]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 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, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], { [0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 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], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[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}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[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}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 1, 1, 2, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[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, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 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, 3, 3, 3, 3, 3, 3] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 7, 7, 7, 7, 7, 7, 7] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 21, 21, 21, 21] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [3, 1, 2], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 1], [4, 3, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2], [1, 2, 3, 4]}} the member , {[1, 3, 2], [2, 1, 3], [3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[3, 0]}, {}], [[1, 1], {[3, 0, 0]}, {1, 2}], [[2, 1], {[0, 2, 0], [2, 1, 0], [0, 1, 1]}, {}], [[1, 2], {[3, 1, 0], [0, 2, 0]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [ [1, 2, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [2, 0, 1, 0]}, {1, 3} ], [[1, 2, 3], {[3, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 1], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [2, 0, 1, 0]}, {2, 3} ], [ [2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 3} ], [[3, 2, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [3, 1, 1, 0, 0]}, {3, 4}] , [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [2, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[1, 2, 3, 1], { [0, 0, 1, 2, 0], [2, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[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, 3, 1, 1], { [0, 0, 1, 2, 0], [2, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 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, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], { [0, 0, 1, 2, 0], [0, 0, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}]] 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, 8, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 7, 7, 7, 7] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [3, 2, 1], [2, 1, 4, 3]}, {[1, 2, 3], [3, 1, 2], [3, 2, 1], [2, 1, 4, 3]}, {[1, 2, 3], [1, 3, 2], [3, 2, 1], [3, 4, 1, 2]}, {[1, 2, 3], [2, 1, 3], [3, 2, 1], [3, 4, 1, 2]}} the member , {[1, 2, 3], [2, 3, 1], [3, 2, 1], [2, 1, 4, 3]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 2], [2, 1], [3, 0], [0, 3]}, {}], [[1, 1], { [2, 1, 0], [1, 1, 1], [1, 2, 0], [3, 0, 0], [0, 3, 0], [2, 0, 1], [0, 2, 1], [1, 0, 2], [0, 1, 2], [0, 0, 3]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 1, 1], [0, 3, 0]}, {}], [[2, 1], {[1, 1, 0], [0, 3, 0], [0, 2, 1], [0, 1, 2]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {2, 3} ], [ [1, 2, 1], {[0, 0, 3, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 1, 0]}, {1, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], %2, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 3} ], [[2, 1, 1], {[0, 0, 3, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 1, 2], [1, 0, 1, 0]}, {2, 3}], [[2, 1, 3], %2, {}], [[3, 1, 2], %2, {}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[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, 2], %1, {3, 4}], [[2, 4, 3, 1], {[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, 1, 2, 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, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 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], %1, {1}], [[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[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], %1, {3, 4}] ] %1 := {[0, 1, 0, 1, 1], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0]} %2 := {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 0, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 0, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 23, 0, 0, 0, 0] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [3, 2, 1], [4, 1, 2, 3]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2], [3, 2, 1, 4]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1], [1, 4, 3, 2]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1], [2, 3, 4, 1]}} the member , {[2, 1, 3], [2, 3, 1], [3, 2, 1], [4, 1, 2, 3]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[1, 1], [3, 0]}, {}], [[2, 1], {[1, 1, 0], [0, 1, 1], [0, 3, 0]}, {2}], [[1, 2], {[0, 4, 0], [1, 1, 0], [0, 2, 1]}, {1}], [[1, 1], {[1, 1, 0], [1, 0, 1], [3, 0, 0]}, {1, 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] Out of a total of , 20, cases 20, were successful and , 0, failed Success Rate: , 1. Here are the failures {}