Identifier
Values
[[1],[1],[1]] => [1,1,1] => [1,1] => [1] => 1
[[1],[1],[1],[1]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[2],[1],[1]] => [2,1,1] => [1,1] => [1] => 1
[[1,1],[1],[1]] => [2,1,1] => [1,1] => [1] => 1
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2],[1],[1],[1]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[2],[2],[1]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[1],[1],[1]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1],[1,1],[1]] => [2,2,1] => [2,1] => [1] => 1
[[3],[1],[1]] => [3,1,1] => [1,1] => [1] => 1
[[2,1],[1],[1]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,1],[1],[1]] => [3,1,1] => [1,1] => [1] => 1
[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2],[2],[1],[1]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[2],[2],[2]] => [2,2,2] => [2,2] => [2] => 2
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1],[1,1],[1,1]] => [2,2,2] => [2,2] => [2] => 2
[[3],[1],[1],[1]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[3],[2],[1]] => [3,2,1] => [2,1] => [1] => 1
[[2,1],[1],[1],[1]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[2,1],[2],[1]] => [3,2,1] => [2,1] => [1] => 1
[[2,1],[1,1],[1]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1],[1,1],[1]] => [3,2,1] => [2,1] => [1] => 1
[[4],[1],[1]] => [4,1,1] => [1,1] => [1] => 1
[[3,1],[1],[1]] => [4,1,1] => [1,1] => [1] => 1
[[2,2],[1],[1]] => [4,1,1] => [1,1] => [1] => 1
[[2,1,1],[1],[1]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,1],[1],[1]] => [4,1,1] => [1,1] => [1] => 1
[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2],[2],[2],[1]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[3],[2],[1],[1]] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[[3],[2],[2]] => [3,2,2] => [2,2] => [2] => 2
[[3],[3],[1]] => [3,3,1] => [3,1] => [1] => 1
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,1],[2],[1],[1]] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1],[2],[2]] => [3,2,2] => [2,2] => [2] => 2
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1],[1,1],[1,1]] => [3,2,2] => [2,2] => [2] => 2
[[2,1],[2,1],[1]] => [3,3,1] => [3,1] => [1] => 1
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1,1],[1,1],[1,1]] => [3,2,2] => [2,2] => [2] => 2
[[1,1,1],[1,1,1],[1]] => [3,3,1] => [3,1] => [1] => 1
[[4],[1],[1],[1]] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[[4],[2],[1]] => [4,2,1] => [2,1] => [1] => 1
[[3,1],[1],[1],[1]] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[[3,1],[2],[1]] => [4,2,1] => [2,1] => [1] => 1
[[3,1],[1,1],[1]] => [4,2,1] => [2,1] => [1] => 1
[[2,2],[1],[1],[1]] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[[2,2],[2],[1]] => [4,2,1] => [2,1] => [1] => 1
[[2,2],[1,1],[1]] => [4,2,1] => [2,1] => [1] => 1
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[[2,1,1],[2],[1]] => [4,2,1] => [2,1] => [1] => 1
[[2,1,1],[1,1],[1]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1,1],[1,1],[1]] => [4,2,1] => [2,1] => [1] => 1
[[5],[1],[1]] => [5,1,1] => [1,1] => [1] => 1
[[4,1],[1],[1]] => [5,1,1] => [1,1] => [1] => 1
[[3,2],[1],[1]] => [5,1,1] => [1,1] => [1] => 1
[[3,1,1],[1],[1]] => [5,1,1] => [1,1] => [1] => 1
[[2,2,1],[1],[1]] => [5,1,1] => [1,1] => [1] => 1
[[2,1,1,1],[1],[1]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,1,1,1],[1],[1]] => [5,1,1] => [1,1] => [1] => 1
[[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2],[2],[1],[1],[1],[1]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[2],[2],[2],[2]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[1,1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1],[1,1],[1],[1],[1],[1]] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[[3],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[3],[2],[2],[1]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[3],[3],[1],[1]] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[[3],[3],[2]] => [3,3,2] => [3,2] => [2] => 2
[[2,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,1],[2],[2],[1]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[[2,1],[2,1],[2]] => [3,3,2] => [3,2] => [2] => 2
[[2,1],[2,1],[1,1]] => [3,3,2] => [3,2] => [2] => 2
[[1,1,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => [3,2] => [2] => 2
[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[4],[2],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
>>> Load all 643 entries. <<<
[[4],[2],[2]] => [4,2,2] => [2,2] => [2] => 2
[[4],[3],[1]] => [4,3,1] => [3,1] => [1] => 1
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[3,1],[2],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[[3,1],[2],[2]] => [4,2,2] => [2,2] => [2] => 2
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[[3,1],[1,1],[1,1]] => [4,2,2] => [2,2] => [2] => 2
[[3,1],[3],[1]] => [4,3,1] => [3,1] => [1] => 1
[[3,1],[2,1],[1]] => [4,3,1] => [3,1] => [1] => 1
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,2],[2],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2],[2],[2]] => [4,2,2] => [2,2] => [2] => 2
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2],[1,1],[1,1]] => [4,2,2] => [2,2] => [2] => 2
[[2,2],[2,1],[1]] => [4,3,1] => [3,1] => [1] => 1
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1,1],[2],[2]] => [4,2,2] => [2,2] => [2] => 2
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1,1],[1,1],[1,1]] => [4,2,2] => [2,2] => [2] => 2
[[2,1,1],[2,1],[1]] => [4,3,1] => [3,1] => [1] => 1
[[2,1,1],[1,1,1],[1]] => [4,3,1] => [3,1] => [1] => 1
[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => [2,2] => [2] => 2
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => [3,1] => [1] => 1
[[5],[1],[1],[1]] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[[5],[2],[1]] => [5,2,1] => [2,1] => [1] => 1
[[4,1],[1],[1],[1]] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[[4,1],[2],[1]] => [5,2,1] => [2,1] => [1] => 1
[[4,1],[1,1],[1]] => [5,2,1] => [2,1] => [1] => 1
[[3,2],[1],[1],[1]] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[[3,2],[2],[1]] => [5,2,1] => [2,1] => [1] => 1
[[3,2],[1,1],[1]] => [5,2,1] => [2,1] => [1] => 1
[[3,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[[3,1,1],[2],[1]] => [5,2,1] => [2,1] => [1] => 1
[[3,1,1],[1,1],[1]] => [5,2,1] => [2,1] => [1] => 1
[[2,2,1],[1],[1],[1]] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[[2,2,1],[2],[1]] => [5,2,1] => [2,1] => [1] => 1
[[2,2,1],[1,1],[1]] => [5,2,1] => [2,1] => [1] => 1
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[[2,1,1,1],[2],[1]] => [5,2,1] => [2,1] => [1] => 1
[[2,1,1,1],[1,1],[1]] => [5,2,1] => [2,1] => [1] => 1
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => [2,1] => [1] => 1
[[6],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[5,1],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[4,2],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[4,1,1],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[3,3],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[3,2,1],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[3,1,1,1],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[2,2,2],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[2,2,1,1],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[2,1,1,1,1],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[1,1,1,1,1,1],[1],[1]] => [6,1,1] => [1,1] => [1] => 1
[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[2],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2],[2],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2],[2],[2],[1],[1],[1]] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1],[1,1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1],[1,1],[1,1],[1],[1],[1]] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[[3],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[3],[2],[2],[2]] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[3],[3],[2],[1]] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[[3],[3],[3]] => [3,3,3] => [3,3] => [3] => 3
[[2,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,1],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[2,1],[2],[2],[2]] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[[2,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[[2,1],[2,1],[2,1]] => [3,3,3] => [3,3] => [3] => 3
[[1,1,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => [3,3] => [3] => 3
[[4],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[4],[2],[2],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[4],[3],[1],[1]] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[[4],[3],[2]] => [4,3,2] => [3,2] => [2] => 2
[[4],[4],[1]] => [4,4,1] => [4,1] => [1] => 1
[[3,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[3,1],[2],[2],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[3,1],[3],[1],[1]] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[[3,1],[3],[2]] => [4,3,2] => [3,2] => [2] => 2
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[[3,1],[2,1],[2]] => [4,3,2] => [3,2] => [2] => 2
[[3,1],[2,1],[1,1]] => [4,3,2] => [3,2] => [2] => 2
[[3,1],[3,1],[1]] => [4,4,1] => [4,1] => [1] => 1
[[2,2],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,2],[2],[2],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[[2,2],[2,1],[2]] => [4,3,2] => [3,2] => [2] => 2
[[2,2],[2,1],[1,1]] => [4,3,2] => [3,2] => [2] => 2
[[2,2],[2,2],[1]] => [4,4,1] => [4,1] => [1] => 1
[[2,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[[2,1,1],[2,1],[2]] => [4,3,2] => [3,2] => [2] => 2
[[2,1,1],[2,1],[1,1]] => [4,3,2] => [3,2] => [2] => 2
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => [3,2] => [2] => 2
[[2,1,1],[2,1,1],[1]] => [4,4,1] => [4,1] => [1] => 1
[[1,1,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => [3,2] => [2] => 2
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => [4,1] => [1] => 1
[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[5],[2],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[5],[2],[2]] => [5,2,2] => [2,2] => [2] => 2
[[5],[3],[1]] => [5,3,1] => [3,1] => [1] => 1
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[4,1],[2],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[4,1],[2],[2]] => [5,2,2] => [2,2] => [2] => 2
[[4,1],[1,1],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[4,1],[1,1],[1,1]] => [5,2,2] => [2,2] => [2] => 2
[[4,1],[3],[1]] => [5,3,1] => [3,1] => [1] => 1
[[4,1],[2,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[3,2],[2],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[3,2],[2],[2]] => [5,2,2] => [2,2] => [2] => 2
[[3,2],[1,1],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[3,2],[1,1],[1,1]] => [5,2,2] => [2,2] => [2] => 2
[[3,2],[3],[1]] => [5,3,1] => [3,1] => [1] => 1
[[3,2],[2,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[3,1,1],[2],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[3,1,1],[2],[2]] => [5,2,2] => [2,2] => [2] => 2
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[3,1,1],[1,1],[1,1]] => [5,2,2] => [2,2] => [2] => 2
[[3,1,1],[3],[1]] => [5,3,1] => [3,1] => [1] => 1
[[3,1,1],[2,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[3,1,1],[1,1,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,2,1],[2],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2,1],[2],[2]] => [5,2,2] => [2,2] => [2] => 2
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2,1],[1,1],[1,1]] => [5,2,2] => [2,2] => [2] => 2
[[2,2,1],[2,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[2,2,1],[1,1,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1,1,1],[2],[2]] => [5,2,2] => [2,2] => [2] => 2
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => [2,2] => [2] => 2
[[2,1,1,1],[2,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => [2,2] => [2] => 2
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => [3,1] => [1] => 1
[[6],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[6],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[5,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[5,1],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[5,1],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[4,2],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[4,2],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[4,2],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[4,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[4,1,1],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[4,1,1],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[3,3],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[3,3],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[3,3],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[3,2,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[3,2,1],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[3,2,1],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[3,1,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[3,1,1,1],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[3,1,1,1],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[2,2,2],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[2,2,2],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[2,2,2],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[2,2,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[2,2,1,1],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[2,2,1,1],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[2,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[2,1,1,1,1],[2],[1]] => [6,2,1] => [2,1] => [1] => 1
[[2,1,1,1,1],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[1,1,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1] => [2,1] => [1] => 1
[[7],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[6,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[5,2],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[5,1,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[4,3],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[4,2,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[4,1,1,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[3,3,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[3,2,2],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[3,2,1,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[3,1,1,1,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[2,2,2,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[2,2,1,1,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[2,1,1,1,1,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1] => [1,1] => [1] => 1
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[2],[2],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2],[2],[2],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[[2],[2],[2],[2],[1],[1]] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[[2],[2],[2],[2],[2]] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 2
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[[1,1],[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 2
[[3],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[3],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[[3],[3],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[[3],[3],[2],[2]] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[[3],[3],[3],[1]] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[2,1],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,1],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[[2,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[[2,1],[2,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[[2,1],[2,1],[2],[2]] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1],[1,1,1],[1,1],[1],[1]] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[[4],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[4],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[4],[2],[2],[2]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[4],[3],[2],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[4],[3],[3]] => [4,3,3] => [3,3] => [3] => 3
[[4],[4],[1],[1]] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[[4],[4],[2]] => [4,4,2] => [4,2] => [2] => 2
[[3,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[3,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[3,1],[2],[2],[2]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[3,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[3,1],[3],[2],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[3,1],[3],[3]] => [4,3,3] => [3,3] => [3] => 3
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[3,1],[2,1],[2,1]] => [4,3,3] => [3,3] => [3] => 3
[[3,1],[3,1],[1],[1]] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[[3,1],[3,1],[2]] => [4,4,2] => [4,2] => [2] => 2
[[3,1],[3,1],[1,1]] => [4,4,2] => [4,2] => [2] => 2
[[2,2],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,2],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[2,2],[2],[2],[2]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[2,2],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[2,2],[2,1],[2,1]] => [4,3,3] => [3,3] => [3] => 3
[[2,2],[2,2],[1],[1]] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[[2,2],[2,2],[2]] => [4,4,2] => [4,2] => [2] => 2
[[2,2],[2,2],[1,1]] => [4,4,2] => [4,2] => [2] => 2
[[2,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[2,1,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[2,1,1],[2],[2],[2]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[2,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[2,1,1],[2,1],[2,1]] => [4,3,3] => [3,3] => [3] => 3
[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [3,3] => [3] => 3
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[[2,1,1],[2,1,1],[2]] => [4,4,2] => [4,2] => [2] => 2
[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => [4,2] => [2] => 2
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [3,3] => [3] => 3
[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => [4,2] => [2] => 2
[[5],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[5],[2],[2],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[5],[3],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[5],[3],[2]] => [5,3,2] => [3,2] => [2] => 2
[[5],[4],[1]] => [5,4,1] => [4,1] => [1] => 1
[[4,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[4,1],[2],[2],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[4,1],[3],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[4,1],[3],[2]] => [5,3,2] => [3,2] => [2] => 2
[[4,1],[2,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[4,1],[2,1],[2]] => [5,3,2] => [3,2] => [2] => 2
[[4,1],[2,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[4,1],[4],[1]] => [5,4,1] => [4,1] => [1] => 1
[[4,1],[3,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[3,2],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[3,2],[2],[2],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[3,2],[3],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[3,2],[3],[2]] => [5,3,2] => [3,2] => [2] => 2
[[3,2],[2,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[3,2],[2,1],[2]] => [5,3,2] => [3,2] => [2] => 2
[[3,2],[2,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[3,2],[3,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[3,2],[2,2],[1]] => [5,4,1] => [4,1] => [1] => 1
[[3,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[3,1,1],[2],[2],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[3,1,1],[3],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[3,1,1],[3],[2]] => [5,3,2] => [3,2] => [2] => 2
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[3,1,1],[2,1],[2]] => [5,3,2] => [3,2] => [2] => 2
[[3,1,1],[2,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[3,1,1],[3,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[3,1,1],[2,1,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[2,2,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,2,1],[2],[2],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[2,2,1],[2,1],[2]] => [5,3,2] => [3,2] => [2] => 2
[[2,2,1],[2,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[2,2,1],[2,2],[1]] => [5,4,1] => [4,1] => [1] => 1
[[2,2,1],[2,1,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[2,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[2,1,1,1],[2,1],[2]] => [5,3,2] => [3,2] => [2] => 2
[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [3,2] => [2] => 2
[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [4,1] => [1] => 1
[[6],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[6],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[6],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[6],[3],[1]] => [6,3,1] => [3,1] => [1] => 1
[[5,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[5,1],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[5,1],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[5,1],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[5,1],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[5,1],[3],[1]] => [6,3,1] => [3,1] => [1] => 1
[[5,1],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[4,2],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[4,2],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[4,2],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[4,2],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[4,2],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[4,2],[3],[1]] => [6,3,1] => [3,1] => [1] => 1
[[4,2],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[4,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[4,1,1],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[4,1,1],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[4,1,1],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[4,1,1],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[4,1,1],[3],[1]] => [6,3,1] => [3,1] => [1] => 1
[[4,1,1],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[4,1,1],[1,1,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,3],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[3,3],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[3,3],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[3,3],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[3,3],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[3,3],[3],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,3],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,2,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[3,2,1],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[3,2,1],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[3,2,1],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[3,2,1],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[3,2,1],[3],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,2,1],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,2,1],[1,1,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[3,1,1,1],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[3,1,1,1],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[3,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[3,1,1,1],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[3,1,1,1],[3],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,1,1,1],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[3,1,1,1],[1,1,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[2,2,2],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,2,2],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2,2],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[2,2,2],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2,2],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[2,2,2],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[2,2,2],[1,1,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[2,2,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,2,1,1],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2,1,1],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[2,2,1,1],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[2,2,1,1],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[2,2,1,1],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[2,2,1,1],[1,1,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[2,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[2,1,1,1,1],[2],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1,1,1,1],[2],[2]] => [6,2,2] => [2,2] => [2] => 2
[[2,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[2,1,1,1,1],[2,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,1,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [2,2] => [2] => 2
[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [3,1] => [1] => 1
[[7],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[7],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[6,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[6,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[6,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[5,2],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[5,2],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[5,2],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[5,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[5,1,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[5,1,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[4,3],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[4,3],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[4,3],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[4,2,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[4,2,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[4,2,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[4,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[4,1,1,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[4,1,1,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,3,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[3,3,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,3,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,2,2],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[3,2,2],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,2,2],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,2,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[3,2,1,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,2,1,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[3,1,1,1,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[3,1,1,1,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[2,2,2,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[2,2,2,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[2,2,2,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[2,2,1,1,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[2,2,1,1,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[2,1,1,1,1,1],[2],[1]] => [7,2,1] => [2,1] => [1] => 1
[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [2,1] => [1] => 1
[[8],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[7,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[6,2],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[6,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[5,3],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[5,2,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[5,1,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[4,4],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[4,3,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[4,2,2],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[4,2,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[4,1,1,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[3,3,2],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[3,3,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[3,2,2,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[3,2,1,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[3,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[2,2,2,2],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[2,2,2,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[2,2,1,1,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1] => [1] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The Cartan determinant of the integer partition.
Let $p=[p_1,...,p_r]$ be a given integer partition with highest part t. Let $A=K[x]/(x^t)$ be the finite dimensional algebra over the field $K$ and $M$ the direct sum of the indecomposable $A$-modules of vector space dimension $p_i$ for each $i$. Then the Cartan determinant of $p$ is the Cartan determinant of the endomorphism algebra of $M$ over $A$.
Explicitly, this is the determinant of the matrix $\left(\min(\bar p_i, \bar p_j)\right)_{i,j}$, where $\bar p$ is the set of distinct parts of the partition.
Map
first row removal
Description
Removes the first entry of an integer partition
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.