Identifier
Values
[[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[1],[1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 1
[[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 1
[[1,1]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 1
[[1],[1],[1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 1
[[2],[1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 1
[[1,1],[1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 1
[[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 1
[[2,1]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 1
[[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 1
[[1],[1],[1],[1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1
[[2],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 1
[[2],[2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 1
[[1,1],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 1
[[1,1],[1,1]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 1
[[3],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 1
[[2,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 1
[[1,1,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 1
[[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[[3,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[[2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[[2,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 1
[[2],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 1
[[2],[2],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 1
[[1,1],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 1
[[1,1],[1,1],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 1
[[3],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 1
[[3],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 1
[[2,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 1
[[2,1],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 1
[[2,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 1
[[1,1,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 1
[[1,1,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 1
[[4],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 1
[[3,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 1
[[2,2],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 1
[[2,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 1
[[1,1,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 1
[[2],[2],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 1
[[2],[2],[2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 1
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 1
[[1,1],[1,1],[1,1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 1
[[3],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 1
[[3],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 1
[[3],[3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 1
[[2,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 1
[[2,1],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 1
[[2,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 1
[[2,1],[2,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 1
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 1
[[1,1,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 1
[[1,1,1],[1,1,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 1
[[4],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 1
[[4],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[3,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 1
[[3,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[3,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[2,2],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 1
[[2,2],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[2,2],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[2,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 1
[[2,1,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[2,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[1,1,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 1
[[1,1,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 1
[[2],[2],[2],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 1
[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 1
[[3],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 1
[[3],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 1
[[3],[3],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 1
[[2,1],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 1
[[2,1],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 1
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 1
[[2,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 1
[[2,1],[2,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 1
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 1
[[1,1,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 1
[[1,1,1],[1,1,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 1
[[4],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 1
[[4],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[4],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[[3,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 1
[[3,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[3,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[3,1],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[[3,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[[2,2],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 1
[[2,2],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[2,2],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[2,2],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 1
[[2,1,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[2,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[2,1,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[[2,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 1
[[1,1,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[1,1,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 1
[[3],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 1
[[3],[3],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 1
>>> Load all 178 entries. <<<
[[3],[3],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 1
[[2,1],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 1
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 1
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 1
[[2,1],[2,1],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 1
[[2,1],[2,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 1
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 1
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 1
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 1
[[4],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[4],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[4],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[3,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[3,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[3,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[3,1],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[3,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[2,2],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[2,2],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[2,2],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[2,2],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[2,1,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[2,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[2,1,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[2,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => [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
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => [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
[[3],[3],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 1
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 1
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 1
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 1
[[4],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[4],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[4],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[3,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[3,1],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[3,1],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[3,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[3,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[2,2],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[2,2],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[2,2],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[2,1,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[2,1,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => [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
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => [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
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [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
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [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
[[4],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[3,1],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 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
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.
Map
to partition
Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.