Identifier
Values
[(1,2)] => [2,1] => [2] => 1
[(1,2),(3,4)] => [2,1,4,3] => [2,2] => 2
[(1,3),(2,4)] => [3,4,1,2] => [2,2] => 2
[(1,4),(2,3)] => [3,4,2,1] => [4] => 1
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,2,2] => 2
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [2,2,2] => 2
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [4,2] => 2
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [4,2] => 2
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [6] => 1
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [6] => 1
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [4,2] => 2
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [2,2,2] => 2
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [2,2,2] => 2
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,2,2] => 2
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [4,2] => 2
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [4,2] => 2
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [4,2] => 2
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [6] => 1
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [4,2] => 2
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => 2
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [2,2,2,2] => 2
[(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [4,2,2] => 2
[(1,5),(2,3),(4,6),(7,8)] => [3,5,2,6,1,4,8,7] => [4,2,2] => 2
[(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [6,2] => 2
[(1,7),(2,3),(4,5),(6,8)] => [3,5,2,7,4,8,1,6] => [6,2] => 2
[(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [8] => 1
[(1,8),(2,4),(3,5),(6,7)] => [4,5,7,2,3,8,6,1] => [8] => 1
[(1,7),(2,4),(3,5),(6,8)] => [4,5,7,2,3,8,1,6] => [6,2] => 2
[(1,6),(2,4),(3,5),(7,8)] => [4,5,6,2,3,1,8,7] => [6,2] => 2
[(1,5),(2,4),(3,6),(7,8)] => [4,5,6,2,1,3,8,7] => [4,2,2] => 2
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [2,2,2,2] => 2
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [2,2,2,2] => 2
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,2,2,2] => 2
[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [4,2,2] => 2
[(1,3),(2,6),(4,5),(7,8)] => [3,5,1,6,4,2,8,7] => [4,2,2] => 2
[(1,4),(2,6),(3,5),(7,8)] => [4,5,6,1,3,2,8,7] => [4,2,2] => 2
[(1,5),(2,6),(3,4),(7,8)] => [4,5,6,3,1,2,8,7] => [6,2] => 2
[(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [4,2,2] => 2
[(1,7),(2,5),(3,4),(6,8)] => [4,5,7,3,2,8,1,6] => [4,2,2] => 2
[(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [6,2] => 2
[(1,8),(2,6),(3,4),(5,7)] => [4,6,7,3,8,2,5,1] => [6,2] => 2
[(1,7),(2,6),(3,4),(5,8)] => [4,6,7,3,8,2,1,5] => [4,2,2] => 2
[(1,6),(2,7),(3,4),(5,8)] => [4,6,7,3,8,1,2,5] => [6,2] => 2
[(1,5),(2,7),(3,4),(6,8)] => [4,5,7,3,1,8,2,6] => [6,2] => 2
[(1,4),(2,7),(3,5),(6,8)] => [4,5,7,1,3,8,2,6] => [4,2,2] => 2
[(1,3),(2,7),(4,5),(6,8)] => [3,5,1,7,4,8,2,6] => [4,2,2] => 2
[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [4,2,2] => 2
[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [6,2] => 2
[(1,3),(2,8),(4,5),(6,7)] => [3,5,1,7,4,8,6,2] => [6,2] => 2
[(1,4),(2,8),(3,5),(6,7)] => [4,5,7,1,3,8,6,2] => [6,2] => 2
[(1,5),(2,8),(3,4),(6,7)] => [4,5,7,3,1,8,6,2] => [8] => 1
[(1,6),(2,8),(3,4),(5,7)] => [4,6,7,3,8,1,5,2] => [8] => 1
[(1,7),(2,8),(3,4),(5,6)] => [4,6,7,3,8,5,1,2] => [4,4] => 2
[(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [8] => 1
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [8] => 1
[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => [4,4] => 2
[(1,6),(2,8),(3,5),(4,7)] => [5,6,7,8,3,1,4,2] => [8] => 1
[(1,5),(2,8),(3,6),(4,7)] => [5,6,7,8,1,3,4,2] => [6,2] => 2
[(1,4),(2,8),(3,6),(5,7)] => [4,6,7,1,8,3,5,2] => [6,2] => 2
[(1,3),(2,8),(4,6),(5,7)] => [3,6,1,7,8,4,5,2] => [6,2] => 2
[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [6,2] => 2
[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [4,2,2] => 2
[(1,3),(2,7),(4,6),(5,8)] => [3,6,1,7,8,4,2,5] => [4,2,2] => 2
[(1,4),(2,7),(3,6),(5,8)] => [4,6,7,1,8,3,2,5] => [4,2,2] => 2
[(1,5),(2,7),(3,6),(4,8)] => [5,6,7,8,1,3,2,4] => [4,2,2] => 2
[(1,6),(2,7),(3,5),(4,8)] => [5,6,7,8,3,1,2,4] => [6,2] => 2
[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => [4,2,2] => 2
[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [6,2] => 2
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [8] => 1
[(1,7),(2,5),(3,6),(4,8)] => [5,6,7,8,2,3,1,4] => [6,2] => 2
[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => [4,2,2] => 2
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [2,2,2,2] => 2
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [2,2,2,2] => 2
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [2,2,2,2] => 2
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,2,2,2] => 2
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,2,2,2] => 2
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [2,2,2,2] => 2
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [2,2,2,2] => 2
[(1,5),(2,4),(3,7),(6,8)] => [4,5,7,2,1,8,3,6] => [4,2,2] => 2
[(1,6),(2,4),(3,7),(5,8)] => [4,6,7,2,8,1,3,5] => [4,2,2] => 2
[(1,7),(2,4),(3,6),(5,8)] => [4,6,7,2,8,3,1,5] => [6,2] => 2
[(1,8),(2,4),(3,6),(5,7)] => [4,6,7,2,8,3,5,1] => [8] => 1
[(1,8),(2,3),(4,6),(5,7)] => [3,6,2,7,8,4,5,1] => [8] => 1
[(1,7),(2,3),(4,6),(5,8)] => [3,6,2,7,8,4,1,5] => [6,2] => 2
[(1,6),(2,3),(4,7),(5,8)] => [3,6,2,7,8,1,4,5] => [4,2,2] => 2
[(1,5),(2,3),(4,7),(6,8)] => [3,5,2,7,1,8,4,6] => [4,2,2] => 2
[(1,4),(2,3),(5,7),(6,8)] => [3,4,2,1,7,8,5,6] => [4,2,2] => 2
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [2,2,2,2] => 2
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,2,2,2] => 2
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [4,2,2] => 2
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,7,8,6,5] => [4,2,2] => 2
[(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [4,4] => 2
[(1,5),(2,3),(4,8),(6,7)] => [3,5,2,7,1,8,6,4] => [4,4] => 2
[(1,6),(2,3),(4,8),(5,7)] => [3,6,2,7,8,1,5,4] => [4,4] => 2
[(1,7),(2,3),(4,8),(5,6)] => [3,6,2,7,8,5,1,4] => [8] => 1
[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [6,2] => 2
[(1,8),(2,4),(3,7),(5,6)] => [4,6,7,2,8,5,3,1] => [6,2] => 2
[(1,7),(2,4),(3,8),(5,6)] => [4,6,7,2,8,5,1,3] => [8] => 1
[(1,6),(2,4),(3,8),(5,7)] => [4,6,7,2,8,1,5,3] => [4,4] => 2
[(1,5),(2,4),(3,8),(6,7)] => [4,5,7,2,1,8,6,3] => [4,4] => 2
[(1,4),(2,5),(3,8),(6,7)] => [4,5,7,1,2,8,6,3] => [4,2,2] => 2
>>> Load all 297 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,7,2,8,6,4] => [4,2,2] => 2
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [4,2,2] => 2
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [4,2,2] => 2
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,7,8,2,5,4] => [4,2,2] => 2
[(1,4),(2,6),(3,8),(5,7)] => [4,6,7,1,8,2,5,3] => [4,2,2] => 2
[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => [4,2,2] => 2
[(1,6),(2,5),(3,8),(4,7)] => [5,6,7,8,2,1,4,3] => [4,4] => 2
[(1,7),(2,5),(3,8),(4,6)] => [5,6,7,8,2,4,1,3] => [8] => 1
[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [6,2] => 2
[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [4,2,2] => 2
[(1,7),(2,6),(3,8),(4,5)] => [5,6,7,8,4,2,1,3] => [6,2] => 2
[(1,6),(2,7),(3,8),(4,5)] => [5,6,7,8,4,1,2,3] => [8] => 1
[(1,5),(2,7),(3,8),(4,6)] => [5,6,7,8,1,4,2,3] => [6,2] => 2
[(1,4),(2,7),(3,8),(5,6)] => [4,6,7,1,8,5,2,3] => [6,2] => 2
[(1,3),(2,7),(4,8),(5,6)] => [3,6,1,7,8,5,2,4] => [6,2] => 2
[(1,2),(3,7),(4,8),(5,6)] => [2,1,6,7,8,5,3,4] => [6,2] => 2
[(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [4,2,2] => 2
[(1,3),(2,8),(4,7),(5,6)] => [3,6,1,7,8,5,4,2] => [4,2,2] => 2
[(1,4),(2,8),(3,7),(5,6)] => [4,6,7,1,8,5,3,2] => [4,2,2] => 2
[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => [4,2,2] => 2
[(1,6),(2,8),(3,7),(4,5)] => [5,6,7,8,4,1,3,2] => [6,2] => 2
[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => [8] => 1
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [4,4] => 2
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => 2
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [2,2,2,2,2] => 2
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [3,4,2,1,6,5,8,7,10,9] => [4,2,2,2] => 2
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [3,5,2,6,4,1,8,7,10,9] => [6,2,2] => 2
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [3,5,2,7,4,8,6,1,10,9] => [8,2] => 2
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [3,5,2,7,4,9,6,10,8,1] => [10] => 1
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,5,6,4,3,8,7,10,9] => [4,2,2,2] => 2
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [4,5,6,3,2,1,8,7,10,9] => [4,2,2,2] => 2
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [4,5,7,3,2,8,6,1,10,9] => [6,2,2] => 2
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [4,5,7,3,2,9,6,10,8,1] => [8,2] => 2
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,5,7,4,8,6,3,10,9] => [6,2,2] => 2
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [4,6,7,3,8,5,2,1,10,9] => [8,2] => 2
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [4,6,7,3,9,5,2,10,8,1] => [10] => 1
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,5,7,4,9,6,10,8,3] => [8,2] => 2
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [4,6,8,3,9,5,10,7,2,1] => [6,4] => 2
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,7,8,6,5,10,9] => [4,2,2,2] => 2
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [3,4,2,1,7,8,6,5,10,9] => [4,4,2] => 2
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [3,6,2,7,8,5,4,1,10,9] => [6,2,2] => 2
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [3,6,2,7,9,5,4,10,8,1] => [8,2] => 2
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,6,7,8,5,4,3,10,9] => [4,2,2,2] => 2
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [5,6,7,8,4,3,2,1,10,9] => [4,4,2] => 2
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [5,6,7,9,4,3,2,10,8,1] => [6,4] => 2
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,6,7,9,5,4,10,8,3] => [6,2,2] => 2
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [5,6,8,9,4,3,10,7,2,1] => [10] => 1
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,7,9,6,10,8,5] => [6,2,2] => 2
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [3,4,2,1,7,9,6,10,8,5] => [6,4] => 2
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [3,6,2,8,9,5,10,7,4,1] => [10] => 1
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,6,8,9,5,10,7,4,3] => [8,2] => 2
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [5,7,8,9,4,10,6,3,2,1] => [8,2] => 2
[(1,6),(2,10),(3,9),(4,7),(5,8)] => [6,7,8,9,10,1,4,5,3,2] => [8,2] => 2
[(1,6),(2,9),(3,10),(4,7),(5,8)] => [6,7,8,9,10,1,4,5,2,3] => [4,4,2] => 2
[(1,6),(2,10),(3,7),(4,8),(5,9)] => [6,7,8,9,10,1,3,4,5,2] => [8,2] => 2
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [2,2,2,2,2] => 2
[(1,9),(2,6),(3,7),(4,8),(5,10)] => [6,7,8,9,10,2,3,4,1,5] => [8,2] => 2
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,9,10,8,7] => [4,2,2,2] => 2
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [3,4,2,1,6,5,9,10,8,7] => [4,4,2] => 2
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [3,5,2,6,4,1,9,10,8,7] => [6,4] => 2
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [3,5,2,8,4,9,10,7,6,1] => [8,2] => 2
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,5,6,4,3,9,10,8,7] => [4,4,2] => 2
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [4,5,6,3,2,1,9,10,8,7] => [4,4,2] => 2
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [4,5,8,3,2,9,10,7,6,1] => [6,2,2] => 2
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,5,8,4,9,10,7,6,3] => [6,2,2] => 2
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [4,7,8,3,9,10,6,5,2,1] => [10] => 1
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,8,9,10,7,6,5] => [4,2,2,2] => 2
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [3,4,2,1,8,9,10,7,6,5] => [4,4,2] => 2
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [3,7,2,8,9,10,6,5,4,1] => [6,4] => 2
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,7,8,9,10,6,5,4,3] => [4,4,2] => 2
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [6,7,8,9,10,1,5,4,3,2] => [4,4,2] => 2
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [6,7,8,9,10,5,4,3,2,1] => [4,4,2] => 2
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [7,8,9,10,11,12,6,5,4,3,2,1] => [4,4,4] => 3
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,7,8,9,10,6,5,4,3,12,11] => [4,4,2,2] => 2
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [3,7,2,8,9,11,6,5,4,12,10,1] => [8,4] => 2
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,7,8,9,11,6,5,4,12,10,3] => [6,4,2] => 2
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [3,7,2,8,9,10,6,5,4,1,12,11] => [6,4,2] => 2
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [4,7,8,3,10,11,6,5,12,9,2,1] => [8,4] => 2
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [3,7,2,8,10,11,6,5,12,9,4,1] => [12] => 1
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,7,8,10,11,6,5,12,9,4,3] => [10,2] => 2
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [3,4,2,1,7,8,6,5,10,9,12,11] => [4,4,2,2] => 2
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [4,7,8,3,9,11,6,5,2,12,10,1] => [12] => 1
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,7,8,6,5,11,12,10,9] => [4,4,2,2] => 2
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [4,7,8,3,9,10,6,5,2,1,12,11] => [10,2] => 2
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [3,4,2,1,7,8,6,5,11,12,10,9] => [4,4,4] => 3
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [5,7,9,10,4,11,6,12,8,3,2,1] => [8,4] => 2
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,5,7,4,9,6,10,8,3,12,11] => [8,2,2] => 2
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [3,5,2,7,4,9,6,11,8,12,10,1] => [12] => 1
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,5,7,4,9,6,11,8,12,10,3] => [10,2] => 2
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [3,5,2,7,4,9,6,10,8,1,12,11] => [10,2] => 2
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [4,7,9,3,10,11,6,12,8,5,2,1] => [6,4,2] => 2
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,7,9,6,10,8,5,12,11] => [6,2,2,2] => 2
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [3,7,2,9,10,11,6,12,8,5,4,1] => [10,2] => 2
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,7,9,10,11,6,12,8,5,4,3] => [8,2,2] => 2
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [3,4,2,1,7,9,6,10,8,5,12,11] => [6,4,2] => 2
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [4,5,7,3,2,9,6,11,8,12,10,1] => [10,2] => 2
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,7,9,6,11,8,12,10,5] => [8,2,2] => 2
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [4,5,7,3,2,9,6,10,8,1,12,11] => [8,2,2] => 2
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [3,4,2,1,7,9,6,11,8,12,10,5] => [8,4] => 2
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [5,7,8,10,4,11,6,3,12,9,2,1] => [6,4,2] => 2
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,5,7,4,8,6,3,10,9,12,11] => [6,2,2,2] => 2
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [3,5,2,7,4,10,6,11,12,9,8,1] => [10,2] => 2
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,5,7,4,10,6,11,12,9,8,3] => [8,2,2] => 2
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [3,5,2,7,4,8,6,1,10,9,12,11] => [8,2,2] => 2
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [5,7,8,9,4,11,6,3,2,12,10,1] => [10,2] => 2
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,5,7,4,8,6,3,11,12,10,9] => [6,4,2] => 2
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [5,7,8,9,4,10,6,3,2,1,12,11] => [8,2,2] => 2
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [3,5,2,7,4,8,6,1,11,12,10,9] => [8,4] => 2
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [4,5,7,3,2,10,6,11,12,9,8,1] => [8,2,2] => 2
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,7,10,6,11,12,9,8,5] => [6,2,2,2] => 2
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [4,5,7,3,2,8,6,1,10,9,12,11] => [6,2,2,2] => 2
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [3,4,2,1,7,10,6,11,12,9,8,5] => [6,4,2] => 2
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [4,5,7,3,2,8,6,1,11,12,10,9] => [6,4,2] => 2
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [6,8,9,10,11,5,12,7,4,3,2,1] => [8,4] => 2
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,6,8,9,5,10,7,4,3,12,11] => [8,2,2] => 2
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [3,6,2,8,9,5,11,7,4,12,10,1] => [12] => 1
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,6,8,9,5,11,7,4,12,10,3] => [10,2] => 2
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [3,6,2,8,9,5,10,7,4,1,12,11] => [10,2] => 2
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [4,6,8,3,10,5,11,7,12,9,2,1] => [12] => 1
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => 2
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [3,6,2,8,10,5,11,7,12,9,4,1] => [8,4] => 2
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,6,8,10,5,11,7,12,9,4,3] => [6,4,2] => 2
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [4,6,8,3,9,5,11,7,2,12,10,1] => [8,4] => 2
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [4,6,8,3,9,5,10,7,2,1,12,11] => [6,4,2] => 2
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [3,4,2,1,6,5,8,7,11,12,10,9] => [4,4,2,2] => 2
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [5,8,9,10,4,11,12,7,6,3,2,1] => [12] => 1
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,5,8,4,9,10,7,6,3,12,11] => [6,2,2,2] => 2
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [3,5,2,8,4,9,11,7,6,12,10,1] => [10,2] => 2
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,5,8,4,9,11,7,6,12,10,3] => [8,2,2] => 2
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [3,5,2,8,4,9,10,7,6,1,12,11] => [8,2,2] => 2
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [4,8,9,3,10,11,12,7,6,5,2,1] => [10,2] => 2
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [3,8,2,9,10,11,12,7,6,5,4,1] => [6,4,2] => 2
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,8,9,10,11,12,7,6,5,4,3] => [4,4,2,2] => 2
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [3,4,2,1,8,9,10,7,6,5,12,11] => [4,4,2,2] => 2
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [4,5,8,3,2,9,11,7,6,12,10,1] => [8,2,2] => 2
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,8,9,11,7,6,12,10,5] => [6,2,2,2] => 2
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [4,5,8,3,2,9,10,7,6,1,12,11] => [6,2,2,2] => 2
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [3,4,2,1,8,9,11,7,6,12,10,5] => [6,4,2] => 2
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [5,6,8,10,4,3,11,7,12,9,2,1] => [6,6] => 2
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [3,5,2,8,4,10,11,7,12,9,6,1] => [12] => 1
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,5,8,4,10,11,7,12,9,6,3] => [10,2] => 2
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [3,5,2,6,4,1,8,7,10,9,12,11] => [6,2,2,2] => 2
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [5,6,8,9,4,3,11,7,2,12,10,1] => [12] => 1
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,5,6,4,3,8,7,11,12,10,9] => [4,4,2,2] => 2
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [5,6,8,9,4,3,10,7,2,1,12,11] => [10,2] => 2
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [3,5,2,6,4,1,8,7,11,12,10,9] => [6,4,2] => 2
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [4,5,8,3,2,10,11,7,12,9,6,1] => [10,2] => 2
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,8,10,11,7,12,9,6,5] => [8,2,2] => 2
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [3,4,2,1,8,10,11,7,12,9,6,5] => [8,4] => 2
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [4,5,6,3,2,1,8,7,11,12,10,9] => [4,4,2,2] => 2
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [6,7,9,10,11,5,4,12,8,3,2,1] => [12] => 1
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,6,7,9,5,4,10,8,3,12,11] => [6,2,2,2] => 2
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [3,6,2,7,9,5,4,11,8,12,10,1] => [10,2] => 2
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,6,7,9,5,4,11,8,12,10,3] => [8,2,2] => 2
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [3,6,2,7,9,5,4,10,8,1,12,11] => [8,2,2] => 2
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [4,6,9,3,10,5,11,12,8,7,2,1] => [6,6] => 2
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [3,6,2,9,10,5,11,12,8,7,4,1] => [12] => 1
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,6,9,10,5,11,12,8,7,4,3] => [10,2] => 2
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [3,4,2,1,6,5,9,10,8,7,12,11] => [4,4,2,2] => 2
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [4,6,7,3,9,5,2,11,8,12,10,1] => [12] => 1
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,9,11,8,12,10,7] => [6,2,2,2] => 2
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [4,6,7,3,9,5,2,10,8,1,12,11] => [10,2] => 2
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [3,4,2,1,6,5,9,11,8,12,10,7] => [6,4,2] => 2
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [6,7,8,10,11,5,4,3,12,9,2,1] => [10,2] => 2
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [3,6,2,7,10,5,4,11,12,9,8,1] => [8,2,2] => 2
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,6,7,10,5,4,11,12,9,8,3] => [6,2,2,2] => 2
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [3,6,2,7,8,5,4,1,10,9,12,11] => [6,2,2,2] => 2
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [6,7,8,9,11,5,4,3,2,12,10,1] => [6,4,2] => 2
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,6,7,8,5,4,3,11,12,10,9] => [4,4,2,2] => 2
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [6,7,8,9,10,5,4,3,2,1,12,11] => [4,4,2,2] => 2
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [3,6,2,7,8,5,4,1,11,12,10,9] => [6,4,2] => 2
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [4,6,7,3,10,5,2,11,12,9,8,1] => [10,2] => 2
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [4,6,7,3,8,5,2,1,10,9,12,11] => [8,2,2] => 2
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [3,4,2,1,6,5,10,11,12,9,8,7] => [4,4,2,2] => 2
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [4,6,7,3,8,5,2,1,11,12,10,9] => [8,4] => 2
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [5,6,9,10,4,3,11,12,8,7,2,1] => [12] => 1
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,5,6,4,3,9,10,8,7,12,11] => [4,4,2,2] => 2
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [3,5,2,9,4,10,11,12,8,7,6,1] => [8,4] => 2
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,5,9,4,10,11,12,8,7,6,3] => [6,4,2] => 2
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [3,5,2,6,4,1,9,10,8,7,12,11] => [6,4,2] => 2
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [5,6,7,9,4,3,2,11,8,12,10,1] => [8,4] => 2
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,5,6,4,3,9,11,8,12,10,7] => [6,4,2] => 2
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [5,6,7,9,4,3,2,10,8,1,12,11] => [6,4,2] => 2
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [3,5,2,6,4,1,9,11,8,12,10,7] => [6,6] => 2
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [4,5,9,3,2,10,11,12,8,7,6,1] => [6,4,2] => 2
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,9,10,11,12,8,7,6,5] => [4,4,2,2] => 2
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [4,5,6,3,2,1,9,10,8,7,12,11] => [4,4,2,2] => 2
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [3,4,2,1,9,10,11,12,8,7,6,5] => [4,4,4] => 3
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [4,5,6,3,2,1,9,11,8,12,10,7] => [6,4,2] => 2
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [5,6,7,10,4,3,2,11,12,9,8,1] => [6,4,2] => 2
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,5,6,4,3,10,11,12,9,8,7] => [4,4,2,2] => 2
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [5,6,7,8,4,3,2,1,10,9,12,11] => [4,4,2,2] => 2
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [3,5,2,6,4,1,10,11,12,9,8,7] => [6,4,2] => 2
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [5,6,7,8,4,3,2,1,11,12,10,9] => [4,4,4] => 3
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [4,5,6,3,2,1,10,11,12,9,8,7] => [4,4,2,2] => 2
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [2,2,2,2,2,2] => 2
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Description
The side length of the Durfee square of an integer partition.
Given a partition $\lambda = (\lambda_1,\ldots,\lambda_n)$, the Durfee square is the largest partition $(s^s)$ whose diagram fits inside the diagram of $\lambda$. In symbols, $s = \max\{ i \mid \lambda_i \geq i \}$.
This is also known as the Frobenius rank.
Map
cycle type
Description
The cycle type of a permutation as a partition.
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.