"Welcome to gVATTER, a Maple package for the enumeration of"

           "permutations avoiding generalized permutation patterns."

              "To see a list of available functions, type Help();"

    "or to learn more about a particular function type Help(function_name);"

"There are ", 7, " equivalence classes of generalized patterns of lengths ",

    [3]

                              "Class ", 1, " is:"

                 {{[[1, 2, 3], [0, 0]]}, {[[3, 2, 1], [0, 0]]}}

                             {[[1, 2, 3], [0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 0]]}, {[[3, 2, 1], [0, 0]]}},

    " the pattern set ", {[[1, 2, 3], [0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 70, 349, 2017, 13358, 99377, 822041, 7477162, 74207209, 797771521,

    9236662346, 114579019469, 1516103040833, 21314681315998, 317288088082405,

    4985505271920097, 82459612672301846]

                                       ""

                              "Class ", 2, " is:"

                 {{[[1, 2, 3], [1, 1]]}, {[[3, 2, 1], [1, 1]]}}

                             {[[1, 2, 3], [1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]]}, {[[3, 2, 1], [1, 1]]}},

    " the pattern set ", {[[1, 2, 3], [1, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                              "Class ", 3, " is:"

{{[[1, 2, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]]}, {[[3, 2, 1], [0, 1]]},

    {[[3, 2, 1], [1, 0]]}}

                             {[[1, 2, 3], [0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]]}, {[[1, 2, 3], [1, 0]]},

    {[[3, 2, 1], [0, 1]]}, {[[3, 2, 1], [1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437,

    190899322, 1382958545, 10480142147, 82864869804, 682076806159,

    5832742205057, 51724158235372]

                                       ""

                              "Class ", 4, " is:"

{{[[1, 3, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]]}, {[[2, 3, 1], [0, 0]]},

    {[[3, 1, 2], [0, 0]]}}

                             {[[1, 3, 2], [0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]]}, {[[2, 1, 3], [0, 0]]},

    {[[2, 3, 1], [0, 0]]}, {[[3, 1, 2], [0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 63, 296, 1623, 10176, 71793, 562848, 4853949, 45664896, 465403791,

    5108121216, 60069714207, 753492215808, 10042248398625, 141712039383552,

    2110880441637045, 33097631526180864]

                                       ""

                              "Class ", 5, " is:"

{{[[1, 3, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]]}, {[[2, 3, 1], [1, 0]]},

    {[[3, 1, 2], [0, 1]]}}

                             {[[1, 3, 2], [0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]]}, {[[2, 1, 3], [1, 0]]},

    {[[2, 3, 1], [1, 0]]}, {[[3, 1, 2], [0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                              "Class ", 6, " is:"

{{[[1, 3, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]]}, {[[2, 3, 1], [0, 1]]},

    {[[3, 1, 2], [1, 0]]}}

                             {[[1, 3, 2], [1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]]}, {[[2, 1, 3], [0, 1]]},

    {[[2, 3, 1], [0, 1]]}, {[[3, 1, 2], [1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437,

    190899322, 1382958545, 10480142147, 82864869804, 682076806159,

    5832742205057, 51724158235372]

                                       ""

                              "Class ", 7, " is:"

{{[[1, 3, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]]}, {[[2, 3, 1], [1, 1]]},

    {[[3, 1, 2], [1, 1]]}}

                             {[[1, 3, 2], [1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]]}, {[[2, 1, 3], [1, 1]]},

    {[[2, 3, 1], [1, 1]]}, {[[3, 1, 2], [1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

"Out of the ", 7, " equivalence classes ", 7, "(or ", 100.,

    " %) classes have enumeration schemes."

0, "(or ", 0., " %) classes do not have enumeration schemes of depth <=", 5,

    ", with gap vectors of weight <=", 2

                        "The classes that failed are: "

                                       {}