Identifier
Values
[1] => [1] => [1,0] => [(1,2)] => 1
[1,2] => [2,1] => [1,1,0,0] => [(1,4),(2,3)] => 1
[2,1] => [1,2] => [1,0,1,0] => [(1,2),(3,4)] => 1
[1,2,3] => [2,3,1] => [1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => 1
[1,3,2] => [2,1,3] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 1
[2,1,3] => [3,2,1] => [1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => 1
[2,3,1] => [3,1,2] => [1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => 1
[3,1,2] => [1,3,2] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 1
[3,2,1] => [1,2,3] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 1
[1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => 1
[1,2,4,3] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 1
[1,3,2,4] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => 1
[1,3,4,2] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => 1
[1,4,2,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 1
[1,4,3,2] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 1
[2,1,3,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => 1
[2,1,4,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 1
[2,3,1,4] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => 1
[2,3,4,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => 1
[2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => 1
[2,4,3,1] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 1
[3,1,2,4] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 1
[3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 1
[3,2,1,4] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 1
[3,2,4,1] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 1
[3,4,1,2] => [4,1,3,2] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 1
[3,4,2,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 1
[4,1,2,3] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 1
[4,1,3,2] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 1
[4,2,1,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 1
[4,2,3,1] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 1
[4,3,1,2] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 1
[4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 1
[1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => 1
[1,2,3,5,4] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[1,2,4,3,5] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => 1
[1,2,4,5,3] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => 1
[1,2,5,3,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 1
[1,2,5,4,3] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[1,3,2,4,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => 1
[1,3,2,5,4] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 1
[1,3,4,2,5] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => 1
[1,3,4,5,2] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => 1
[1,3,5,2,4] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => 1
[1,3,5,4,2] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 1
[1,4,2,3,5] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 1
[1,4,2,5,3] => [2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 1
[1,4,3,2,5] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 1
[1,4,3,5,2] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 1
[1,4,5,2,3] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 1
[1,4,5,3,2] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 1
[1,5,2,3,4] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 1
[1,5,2,4,3] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[1,5,3,2,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 1
[1,5,3,4,2] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 1
[1,5,4,2,3] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 1
[1,5,4,3,2] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[2,1,3,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => 1
[2,1,3,5,4] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[2,1,4,3,5] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 1
[2,1,4,5,3] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 1
[2,1,5,3,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 1
[2,1,5,4,3] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[2,3,1,4,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => 1
[2,3,1,5,4] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 1
[2,3,4,1,5] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => 1
[2,3,4,5,1] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => 1
[2,3,5,1,4] => [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => 1
[2,3,5,4,1] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 1
[2,4,1,3,5] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 1
[2,4,1,5,3] => [3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 1
[2,4,3,1,5] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 1
[2,4,3,5,1] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 1
[2,4,5,1,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 1
[2,4,5,3,1] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 1
[2,5,1,3,4] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => 1
[2,5,1,4,3] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[2,5,3,1,4] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 1
[2,5,3,4,1] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 1
[2,5,4,1,3] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 1
[2,5,4,3,1] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[3,1,2,4,5] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 1
[3,1,2,5,4] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[3,1,4,2,5] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 1
[3,1,4,5,2] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 1
[3,1,5,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 1
[3,1,5,4,2] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[3,2,1,4,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 1
[3,2,1,5,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[3,2,4,1,5] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 1
[3,2,4,5,1] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 1
[3,2,5,1,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 1
[3,2,5,4,1] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[3,4,1,2,5] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 1
[3,4,1,5,2] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 1
[3,4,2,1,5] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 1
[3,4,2,5,1] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 1
[3,4,5,1,2] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 1
[3,4,5,2,1] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 1
[3,5,1,2,4] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 1
[3,5,1,4,2] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
>>> Load all 177 entries. <<<
[3,5,2,1,4] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 1
[3,5,2,4,1] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 1
[3,5,4,1,2] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 1
[3,5,4,2,1] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[4,1,2,3,5] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,1,2,5,3] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,1,3,2,5] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,1,3,5,2] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,1,5,2,3] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,1,5,3,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,2,1,3,5] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,2,1,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,2,3,1,5] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,2,3,5,1] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,2,5,1,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,2,5,3,1] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,3,1,2,5] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,3,1,5,2] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,3,2,1,5] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,3,2,5,1] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,3,5,1,2] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,3,5,2,1] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,5,1,2,3] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,5,1,3,2] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,5,2,1,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,5,2,3,1] => [5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,5,3,1,2] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[4,5,3,2,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[5,1,2,3,4] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 1
[5,1,2,4,3] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[5,1,3,2,4] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 1
[5,1,3,4,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 1
[5,1,4,2,3] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 1
[5,1,4,3,2] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[5,2,1,3,4] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 1
[5,2,1,4,3] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 1
[5,2,3,1,4] => [1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 1
[5,2,3,4,1] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 1
[5,2,4,1,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 1
[5,2,4,3,1] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 1
[5,3,1,2,4] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1
[5,3,1,4,2] => [1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1
[5,3,2,1,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1
[5,3,2,4,1] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1
[5,3,4,1,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1
[5,3,4,2,1] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1
[5,4,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 1
[5,4,1,3,2] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[5,4,2,1,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 1
[5,4,2,3,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 1
[5,4,3,1,2] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 1
[5,4,3,2,1] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[6,5,1,2,3,4] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 1
[6,5,1,2,4,3] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 1
[6,5,1,3,2,4] => [1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 1
[6,5,1,3,4,2] => [1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 1
[6,5,1,4,2,3] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 1
[6,5,1,4,3,2] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 1
[6,5,2,1,3,4] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 1
[6,5,2,1,4,3] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 1
[6,5,2,3,1,4] => [1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 1
[6,5,2,3,4,1] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 1
[6,5,2,4,1,3] => [1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 1
[6,5,2,4,3,1] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 1
[6,5,3,1,2,4] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 1
[6,5,3,1,4,2] => [1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 1
[6,5,3,2,1,4] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 1
[6,5,3,2,4,1] => [1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 1
[6,5,3,4,1,2] => [1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 1
[6,5,3,4,2,1] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 1
[6,5,4,1,2,3] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 1
[6,5,4,1,3,2] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 1
[6,5,4,2,1,3] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 1
[6,5,4,2,3,1] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 1
[6,5,4,3,1,2] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 1
[6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of nesting-similar perfect matchings of a perfect matching.
Consider the infinite tree $T$ defined in [1] as follows. $T$ has the perfect matchings on $\{1,\dots,2n\}$ on level $n$, with children obtained by inserting an arc with opener $1$. For example, the matching $[(1,2)]$ has the three children $[(1,2),(3,4)]$, $[(1,3),(2,4)]$ and $[(1,4),(2,3)]$.
Two perfect matchings $M$ and $N$ on $\{1,\dots,2n\}$ are nesting-similar, if the distribution of the number of nestings agrees on all levels of the subtrees of $T$ rooted at $M$ and $N$.
[thm 1.2, 1] shows that to find out whether $M$ and $N$ are nesting-similar, it is enough to check that $M$ and $N$ have the same number of nestings, and that the distribution of nestings agrees for their direct children.
[thm 3.5, 1], see also [2], gives the number of equivalence classes of nesting-similar matchings with $n$ arcs as $$2\cdot 4^{n-1} - \frac{3n-1}{2n+2}\binom{2n}{n}.$$ [prop 3.6, 1] has further interpretations of this number.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.