Identifier
- St001446: Plane partitions ⟶ ℤ
Values
[[1]] => 1
[[1],[1]] => 2
[[2]] => 1
[[1,1]] => 1
[[1],[1],[1]] => 3
[[2],[1]] => 2
[[1,1],[1]] => 2
[[3]] => 1
[[2,1]] => 1
[[1,1,1]] => 1
[[1],[1],[1],[1]] => 4
[[2],[1],[1]] => 3
[[2],[2]] => 2
[[1,1],[1],[1]] => 3
[[1,1],[1,1]] => 2
[[3],[1]] => 2
[[2,1],[1]] => 2
[[1,1,1],[1]] => 2
[[4]] => 1
[[3,1]] => 1
[[2,2]] => 1
[[2,1,1]] => 1
[[1,1,1,1]] => 1
[[1],[1],[1],[1],[1]] => 5
[[2],[1],[1],[1]] => 4
[[2],[2],[1]] => 3
[[1,1],[1],[1],[1]] => 4
[[1,1],[1,1],[1]] => 3
[[3],[1],[1]] => 3
[[3],[2]] => 2
[[2,1],[1],[1]] => 3
[[2,1],[2]] => 2
[[2,1],[1,1]] => 2
[[1,1,1],[1],[1]] => 3
[[1,1,1],[1,1]] => 2
[[4],[1]] => 2
[[3,1],[1]] => 2
[[2,2],[1]] => 2
[[2,1,1],[1]] => 2
[[1,1,1,1],[1]] => 2
[[5]] => 1
[[4,1]] => 1
[[3,2]] => 1
[[3,1,1]] => 1
[[2,2,1]] => 1
[[2,1,1,1]] => 1
[[1,1,1,1,1]] => 1
[[1],[1],[1],[1],[1],[1]] => 6
[[2],[1],[1],[1],[1]] => 5
[[2],[2],[1],[1]] => 4
[[2],[2],[2]] => 3
[[1,1],[1],[1],[1],[1]] => 5
[[1,1],[1,1],[1],[1]] => 4
[[1,1],[1,1],[1,1]] => 3
[[3],[1],[1],[1]] => 4
[[3],[2],[1]] => 3
[[3],[3]] => 2
[[2,1],[1],[1],[1]] => 4
[[2,1],[2],[1]] => 3
[[2,1],[1,1],[1]] => 3
[[2,1],[2,1]] => 2
[[1,1,1],[1],[1],[1]] => 4
[[1,1,1],[1,1],[1]] => 3
[[1,1,1],[1,1,1]] => 2
[[4],[1],[1]] => 3
[[4],[2]] => 2
[[3,1],[1],[1]] => 3
[[3,1],[2]] => 2
[[3,1],[1,1]] => 2
[[2,2],[1],[1]] => 3
[[2,2],[2]] => 2
[[2,2],[1,1]] => 2
[[2,1,1],[1],[1]] => 3
[[2,1,1],[2]] => 2
[[2,1,1],[1,1]] => 2
[[1,1,1,1],[1],[1]] => 3
[[1,1,1,1],[1,1]] => 2
[[5],[1]] => 2
[[4,1],[1]] => 2
[[3,2],[1]] => 2
[[3,1,1],[1]] => 2
[[2,2,1],[1]] => 2
[[2,1,1,1],[1]] => 2
[[1,1,1,1,1],[1]] => 2
[[6]] => 1
[[5,1]] => 1
[[4,2]] => 1
[[4,1,1]] => 1
[[3,3]] => 1
[[3,2,1]] => 1
[[3,1,1,1]] => 1
[[2,2,2]] => 1
[[2,2,1,1]] => 1
[[2,1,1,1,1]] => 1
[[1,1,1,1,1,1]] => 1
[[1],[1],[1],[1],[1],[1],[1]] => 7
[[2],[1],[1],[1],[1],[1]] => 6
[[2],[2],[1],[1],[1]] => 5
[[2],[2],[2],[1]] => 4
[[1,1],[1],[1],[1],[1],[1]] => 6
[[1,1],[1,1],[1],[1],[1]] => 5
>>> Load all 1123 entries. <<<[[1,1],[1,1],[1,1],[1]] => 4
[[3],[1],[1],[1],[1]] => 5
[[3],[2],[1],[1]] => 4
[[3],[2],[2]] => 3
[[3],[3],[1]] => 3
[[2,1],[1],[1],[1],[1]] => 5
[[2,1],[2],[1],[1]] => 4
[[2,1],[2],[2]] => 3
[[2,1],[1,1],[1],[1]] => 4
[[2,1],[1,1],[1,1]] => 3
[[2,1],[2,1],[1]] => 3
[[1,1,1],[1],[1],[1],[1]] => 5
[[1,1,1],[1,1],[1],[1]] => 4
[[1,1,1],[1,1],[1,1]] => 3
[[1,1,1],[1,1,1],[1]] => 3
[[4],[1],[1],[1]] => 4
[[4],[2],[1]] => 3
[[4],[3]] => 2
[[3,1],[1],[1],[1]] => 4
[[3,1],[2],[1]] => 3
[[3,1],[1,1],[1]] => 3
[[3,1],[3]] => 2
[[3,1],[2,1]] => 2
[[2,2],[1],[1],[1]] => 4
[[2,2],[2],[1]] => 3
[[2,2],[1,1],[1]] => 3
[[2,2],[2,1]] => 2
[[2,1,1],[1],[1],[1]] => 4
[[2,1,1],[2],[1]] => 3
[[2,1,1],[1,1],[1]] => 3
[[2,1,1],[2,1]] => 2
[[2,1,1],[1,1,1]] => 2
[[1,1,1,1],[1],[1],[1]] => 4
[[1,1,1,1],[1,1],[1]] => 3
[[1,1,1,1],[1,1,1]] => 2
[[5],[1],[1]] => 3
[[5],[2]] => 2
[[4,1],[1],[1]] => 3
[[4,1],[2]] => 2
[[4,1],[1,1]] => 2
[[3,2],[1],[1]] => 3
[[3,2],[2]] => 2
[[3,2],[1,1]] => 2
[[3,1,1],[1],[1]] => 3
[[3,1,1],[2]] => 2
[[3,1,1],[1,1]] => 2
[[2,2,1],[1],[1]] => 3
[[2,2,1],[2]] => 2
[[2,2,1],[1,1]] => 2
[[2,1,1,1],[1],[1]] => 3
[[2,1,1,1],[2]] => 2
[[2,1,1,1],[1,1]] => 2
[[1,1,1,1,1],[1],[1]] => 3
[[1,1,1,1,1],[1,1]] => 2
[[6],[1]] => 2
[[5,1],[1]] => 2
[[4,2],[1]] => 2
[[4,1,1],[1]] => 2
[[3,3],[1]] => 2
[[3,2,1],[1]] => 2
[[3,1,1,1],[1]] => 2
[[2,2,2],[1]] => 2
[[2,2,1,1],[1]] => 2
[[2,1,1,1,1],[1]] => 2
[[1,1,1,1,1,1],[1]] => 2
[[7]] => 1
[[6,1]] => 1
[[5,2]] => 1
[[5,1,1]] => 1
[[4,3]] => 1
[[4,2,1]] => 1
[[4,1,1,1]] => 1
[[3,3,1]] => 1
[[3,2,2]] => 1
[[3,2,1,1]] => 1
[[3,1,1,1,1]] => 1
[[2,2,2,1]] => 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],[1],[1],[1],[1],[1]] => 8
[[2],[1],[1],[1],[1],[1],[1]] => 7
[[2],[2],[1],[1],[1],[1]] => 6
[[2],[2],[2],[1],[1]] => 5
[[2],[2],[2],[2]] => 4
[[1,1],[1],[1],[1],[1],[1],[1]] => 7
[[1,1],[1,1],[1],[1],[1],[1]] => 6
[[1,1],[1,1],[1,1],[1],[1]] => 5
[[1,1],[1,1],[1,1],[1,1]] => 4
[[3],[1],[1],[1],[1],[1]] => 6
[[3],[2],[1],[1],[1]] => 5
[[3],[2],[2],[1]] => 4
[[3],[3],[1],[1]] => 4
[[3],[3],[2]] => 3
[[2,1],[1],[1],[1],[1],[1]] => 6
[[2,1],[2],[1],[1],[1]] => 5
[[2,1],[2],[2],[1]] => 4
[[2,1],[1,1],[1],[1],[1]] => 5
[[2,1],[1,1],[1,1],[1]] => 4
[[2,1],[2,1],[1],[1]] => 4
[[2,1],[2,1],[2]] => 3
[[2,1],[2,1],[1,1]] => 3
[[1,1,1],[1],[1],[1],[1],[1]] => 6
[[1,1,1],[1,1],[1],[1],[1]] => 5
[[1,1,1],[1,1],[1,1],[1]] => 4
[[1,1,1],[1,1,1],[1],[1]] => 4
[[1,1,1],[1,1,1],[1,1]] => 3
[[4],[1],[1],[1],[1]] => 5
[[4],[2],[1],[1]] => 4
[[4],[2],[2]] => 3
[[4],[3],[1]] => 3
[[4],[4]] => 2
[[3,1],[1],[1],[1],[1]] => 5
[[3,1],[2],[1],[1]] => 4
[[3,1],[2],[2]] => 3
[[3,1],[1,1],[1],[1]] => 4
[[3,1],[1,1],[1,1]] => 3
[[3,1],[3],[1]] => 3
[[3,1],[2,1],[1]] => 3
[[3,1],[3,1]] => 2
[[2,2],[1],[1],[1],[1]] => 5
[[2,2],[2],[1],[1]] => 4
[[2,2],[2],[2]] => 3
[[2,2],[1,1],[1],[1]] => 4
[[2,2],[1,1],[1,1]] => 3
[[2,2],[2,1],[1]] => 3
[[2,2],[2,2]] => 2
[[2,1,1],[1],[1],[1],[1]] => 5
[[2,1,1],[2],[1],[1]] => 4
[[2,1,1],[2],[2]] => 3
[[2,1,1],[1,1],[1],[1]] => 4
[[2,1,1],[1,1],[1,1]] => 3
[[2,1,1],[2,1],[1]] => 3
[[2,1,1],[1,1,1],[1]] => 3
[[2,1,1],[2,1,1]] => 2
[[1,1,1,1],[1],[1],[1],[1]] => 5
[[1,1,1,1],[1,1],[1],[1]] => 4
[[1,1,1,1],[1,1],[1,1]] => 3
[[1,1,1,1],[1,1,1],[1]] => 3
[[1,1,1,1],[1,1,1,1]] => 2
[[5],[1],[1],[1]] => 4
[[5],[2],[1]] => 3
[[5],[3]] => 2
[[4,1],[1],[1],[1]] => 4
[[4,1],[2],[1]] => 3
[[4,1],[1,1],[1]] => 3
[[4,1],[3]] => 2
[[4,1],[2,1]] => 2
[[3,2],[1],[1],[1]] => 4
[[3,2],[2],[1]] => 3
[[3,2],[1,1],[1]] => 3
[[3,2],[3]] => 2
[[3,2],[2,1]] => 2
[[3,1,1],[1],[1],[1]] => 4
[[3,1,1],[2],[1]] => 3
[[3,1,1],[1,1],[1]] => 3
[[3,1,1],[3]] => 2
[[3,1,1],[2,1]] => 2
[[3,1,1],[1,1,1]] => 2
[[2,2,1],[1],[1],[1]] => 4
[[2,2,1],[2],[1]] => 3
[[2,2,1],[1,1],[1]] => 3
[[2,2,1],[2,1]] => 2
[[2,2,1],[1,1,1]] => 2
[[2,1,1,1],[1],[1],[1]] => 4
[[2,1,1,1],[2],[1]] => 3
[[2,1,1,1],[1,1],[1]] => 3
[[2,1,1,1],[2,1]] => 2
[[2,1,1,1],[1,1,1]] => 2
[[1,1,1,1,1],[1],[1],[1]] => 4
[[1,1,1,1,1],[1,1],[1]] => 3
[[1,1,1,1,1],[1,1,1]] => 2
[[6],[1],[1]] => 3
[[6],[2]] => 2
[[5,1],[1],[1]] => 3
[[5,1],[2]] => 2
[[5,1],[1,1]] => 2
[[4,2],[1],[1]] => 3
[[4,2],[2]] => 2
[[4,2],[1,1]] => 2
[[4,1,1],[1],[1]] => 3
[[4,1,1],[2]] => 2
[[4,1,1],[1,1]] => 2
[[3,3],[1],[1]] => 3
[[3,3],[2]] => 2
[[3,3],[1,1]] => 2
[[3,2,1],[1],[1]] => 3
[[3,2,1],[2]] => 2
[[3,2,1],[1,1]] => 2
[[3,1,1,1],[1],[1]] => 3
[[3,1,1,1],[2]] => 2
[[3,1,1,1],[1,1]] => 2
[[2,2,2],[1],[1]] => 3
[[2,2,2],[2]] => 2
[[2,2,2],[1,1]] => 2
[[2,2,1,1],[1],[1]] => 3
[[2,2,1,1],[2]] => 2
[[2,2,1,1],[1,1]] => 2
[[2,1,1,1,1],[1],[1]] => 3
[[2,1,1,1,1],[2]] => 2
[[2,1,1,1,1],[1,1]] => 2
[[1,1,1,1,1,1],[1],[1]] => 3
[[1,1,1,1,1,1],[1,1]] => 2
[[7],[1]] => 2
[[6,1],[1]] => 2
[[5,2],[1]] => 2
[[5,1,1],[1]] => 2
[[4,3],[1]] => 2
[[4,2,1],[1]] => 2
[[4,1,1,1],[1]] => 2
[[3,3,1],[1]] => 2
[[3,2,2],[1]] => 2
[[3,2,1,1],[1]] => 2
[[3,1,1,1,1],[1]] => 2
[[2,2,2,1],[1]] => 2
[[2,2,1,1,1],[1]] => 2
[[2,1,1,1,1,1],[1]] => 2
[[1,1,1,1,1,1,1],[1]] => 2
[[8]] => 1
[[7,1]] => 1
[[6,2]] => 1
[[6,1,1]] => 1
[[5,3]] => 1
[[5,2,1]] => 1
[[5,1,1,1]] => 1
[[4,4]] => 1
[[4,3,1]] => 1
[[4,2,2]] => 1
[[4,2,1,1]] => 1
[[4,1,1,1,1]] => 1
[[3,3,2]] => 1
[[3,3,1,1]] => 1
[[3,2,2,1]] => 1
[[3,2,1,1,1]] => 1
[[3,1,1,1,1,1]] => 1
[[2,2,2,2]] => 1
[[2,2,2,1,1]] => 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],[1],[1],[1],[1],[1]] => 9
[[2],[1],[1],[1],[1],[1],[1],[1]] => 8
[[2],[2],[1],[1],[1],[1],[1]] => 7
[[2],[2],[2],[1],[1],[1]] => 6
[[2],[2],[2],[2],[1]] => 5
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => 8
[[1,1],[1,1],[1],[1],[1],[1],[1]] => 7
[[1,1],[1,1],[1,1],[1],[1],[1]] => 6
[[1,1],[1,1],[1,1],[1,1],[1]] => 5
[[3],[1],[1],[1],[1],[1],[1]] => 7
[[3],[2],[1],[1],[1],[1]] => 6
[[3],[2],[2],[1],[1]] => 5
[[3],[2],[2],[2]] => 4
[[3],[3],[1],[1],[1]] => 5
[[3],[3],[2],[1]] => 4
[[3],[3],[3]] => 3
[[2,1],[1],[1],[1],[1],[1],[1]] => 7
[[2,1],[2],[1],[1],[1],[1]] => 6
[[2,1],[2],[2],[1],[1]] => 5
[[2,1],[2],[2],[2]] => 4
[[2,1],[1,1],[1],[1],[1],[1]] => 6
[[2,1],[1,1],[1,1],[1],[1]] => 5
[[2,1],[1,1],[1,1],[1,1]] => 4
[[2,1],[2,1],[1],[1],[1]] => 5
[[2,1],[2,1],[2],[1]] => 4
[[2,1],[2,1],[1,1],[1]] => 4
[[2,1],[2,1],[2,1]] => 3
[[1,1,1],[1],[1],[1],[1],[1],[1]] => 7
[[1,1,1],[1,1],[1],[1],[1],[1]] => 6
[[1,1,1],[1,1],[1,1],[1],[1]] => 5
[[1,1,1],[1,1],[1,1],[1,1]] => 4
[[1,1,1],[1,1,1],[1],[1],[1]] => 5
[[1,1,1],[1,1,1],[1,1],[1]] => 4
[[1,1,1],[1,1,1],[1,1,1]] => 3
[[4],[1],[1],[1],[1],[1]] => 6
[[4],[2],[1],[1],[1]] => 5
[[4],[2],[2],[1]] => 4
[[4],[3],[1],[1]] => 4
[[4],[3],[2]] => 3
[[4],[4],[1]] => 3
[[3,1],[1],[1],[1],[1],[1]] => 6
[[3,1],[2],[1],[1],[1]] => 5
[[3,1],[2],[2],[1]] => 4
[[3,1],[1,1],[1],[1],[1]] => 5
[[3,1],[1,1],[1,1],[1]] => 4
[[3,1],[3],[1],[1]] => 4
[[3,1],[3],[2]] => 3
[[3,1],[2,1],[1],[1]] => 4
[[3,1],[2,1],[2]] => 3
[[3,1],[2,1],[1,1]] => 3
[[3,1],[3,1],[1]] => 3
[[2,2],[1],[1],[1],[1],[1]] => 6
[[2,2],[2],[1],[1],[1]] => 5
[[2,2],[2],[2],[1]] => 4
[[2,2],[1,1],[1],[1],[1]] => 5
[[2,2],[1,1],[1,1],[1]] => 4
[[2,2],[2,1],[1],[1]] => 4
[[2,2],[2,1],[2]] => 3
[[2,2],[2,1],[1,1]] => 3
[[2,2],[2,2],[1]] => 3
[[2,1,1],[1],[1],[1],[1],[1]] => 6
[[2,1,1],[2],[1],[1],[1]] => 5
[[2,1,1],[2],[2],[1]] => 4
[[2,1,1],[1,1],[1],[1],[1]] => 5
[[2,1,1],[1,1],[1,1],[1]] => 4
[[2,1,1],[2,1],[1],[1]] => 4
[[2,1,1],[2,1],[2]] => 3
[[2,1,1],[2,1],[1,1]] => 3
[[2,1,1],[1,1,1],[1],[1]] => 4
[[2,1,1],[1,1,1],[1,1]] => 3
[[2,1,1],[2,1,1],[1]] => 3
[[1,1,1,1],[1],[1],[1],[1],[1]] => 6
[[1,1,1,1],[1,1],[1],[1],[1]] => 5
[[1,1,1,1],[1,1],[1,1],[1]] => 4
[[1,1,1,1],[1,1,1],[1],[1]] => 4
[[1,1,1,1],[1,1,1],[1,1]] => 3
[[1,1,1,1],[1,1,1,1],[1]] => 3
[[5],[1],[1],[1],[1]] => 5
[[5],[2],[1],[1]] => 4
[[5],[2],[2]] => 3
[[5],[3],[1]] => 3
[[5],[4]] => 2
[[4,1],[1],[1],[1],[1]] => 5
[[4,1],[2],[1],[1]] => 4
[[4,1],[2],[2]] => 3
[[4,1],[1,1],[1],[1]] => 4
[[4,1],[1,1],[1,1]] => 3
[[4,1],[3],[1]] => 3
[[4,1],[2,1],[1]] => 3
[[4,1],[4]] => 2
[[4,1],[3,1]] => 2
[[3,2],[1],[1],[1],[1]] => 5
[[3,2],[2],[1],[1]] => 4
[[3,2],[2],[2]] => 3
[[3,2],[1,1],[1],[1]] => 4
[[3,2],[1,1],[1,1]] => 3
[[3,2],[3],[1]] => 3
[[3,2],[2,1],[1]] => 3
[[3,2],[3,1]] => 2
[[3,2],[2,2]] => 2
[[3,1,1],[1],[1],[1],[1]] => 5
[[3,1,1],[2],[1],[1]] => 4
[[3,1,1],[2],[2]] => 3
[[3,1,1],[1,1],[1],[1]] => 4
[[3,1,1],[1,1],[1,1]] => 3
[[3,1,1],[3],[1]] => 3
[[3,1,1],[2,1],[1]] => 3
[[3,1,1],[1,1,1],[1]] => 3
[[3,1,1],[3,1]] => 2
[[3,1,1],[2,1,1]] => 2
[[2,2,1],[1],[1],[1],[1]] => 5
[[2,2,1],[2],[1],[1]] => 4
[[2,2,1],[2],[2]] => 3
[[2,2,1],[1,1],[1],[1]] => 4
[[2,2,1],[1,1],[1,1]] => 3
[[2,2,1],[2,1],[1]] => 3
[[2,2,1],[1,1,1],[1]] => 3
[[2,2,1],[2,2]] => 2
[[2,2,1],[2,1,1]] => 2
[[2,1,1,1],[1],[1],[1],[1]] => 5
[[2,1,1,1],[2],[1],[1]] => 4
[[2,1,1,1],[2],[2]] => 3
[[2,1,1,1],[1,1],[1],[1]] => 4
[[2,1,1,1],[1,1],[1,1]] => 3
[[2,1,1,1],[2,1],[1]] => 3
[[2,1,1,1],[1,1,1],[1]] => 3
[[2,1,1,1],[2,1,1]] => 2
[[2,1,1,1],[1,1,1,1]] => 2
[[1,1,1,1,1],[1],[1],[1],[1]] => 5
[[1,1,1,1,1],[1,1],[1],[1]] => 4
[[1,1,1,1,1],[1,1],[1,1]] => 3
[[1,1,1,1,1],[1,1,1],[1]] => 3
[[1,1,1,1,1],[1,1,1,1]] => 2
[[6],[1],[1],[1]] => 4
[[6],[2],[1]] => 3
[[6],[3]] => 2
[[5,1],[1],[1],[1]] => 4
[[5,1],[2],[1]] => 3
[[5,1],[1,1],[1]] => 3
[[5,1],[3]] => 2
[[5,1],[2,1]] => 2
[[4,2],[1],[1],[1]] => 4
[[4,2],[2],[1]] => 3
[[4,2],[1,1],[1]] => 3
[[4,2],[3]] => 2
[[4,2],[2,1]] => 2
[[4,1,1],[1],[1],[1]] => 4
[[4,1,1],[2],[1]] => 3
[[4,1,1],[1,1],[1]] => 3
[[4,1,1],[3]] => 2
[[4,1,1],[2,1]] => 2
[[4,1,1],[1,1,1]] => 2
[[3,3],[1],[1],[1]] => 4
[[3,3],[2],[1]] => 3
[[3,3],[1,1],[1]] => 3
[[3,3],[3]] => 2
[[3,3],[2,1]] => 2
[[3,2,1],[1],[1],[1]] => 4
[[3,2,1],[2],[1]] => 3
[[3,2,1],[1,1],[1]] => 3
[[3,2,1],[3]] => 2
[[3,2,1],[2,1]] => 2
[[3,2,1],[1,1,1]] => 2
[[3,1,1,1],[1],[1],[1]] => 4
[[3,1,1,1],[2],[1]] => 3
[[3,1,1,1],[1,1],[1]] => 3
[[3,1,1,1],[3]] => 2
[[3,1,1,1],[2,1]] => 2
[[3,1,1,1],[1,1,1]] => 2
[[2,2,2],[1],[1],[1]] => 4
[[2,2,2],[2],[1]] => 3
[[2,2,2],[1,1],[1]] => 3
[[2,2,2],[2,1]] => 2
[[2,2,2],[1,1,1]] => 2
[[2,2,1,1],[1],[1],[1]] => 4
[[2,2,1,1],[2],[1]] => 3
[[2,2,1,1],[1,1],[1]] => 3
[[2,2,1,1],[2,1]] => 2
[[2,2,1,1],[1,1,1]] => 2
[[2,1,1,1,1],[1],[1],[1]] => 4
[[2,1,1,1,1],[2],[1]] => 3
[[2,1,1,1,1],[1,1],[1]] => 3
[[2,1,1,1,1],[2,1]] => 2
[[2,1,1,1,1],[1,1,1]] => 2
[[1,1,1,1,1,1],[1],[1],[1]] => 4
[[1,1,1,1,1,1],[1,1],[1]] => 3
[[1,1,1,1,1,1],[1,1,1]] => 2
[[7],[1],[1]] => 3
[[7],[2]] => 2
[[6,1],[1],[1]] => 3
[[6,1],[2]] => 2
[[6,1],[1,1]] => 2
[[5,2],[1],[1]] => 3
[[5,2],[2]] => 2
[[5,2],[1,1]] => 2
[[5,1,1],[1],[1]] => 3
[[5,1,1],[2]] => 2
[[5,1,1],[1,1]] => 2
[[4,3],[1],[1]] => 3
[[4,3],[2]] => 2
[[4,3],[1,1]] => 2
[[4,2,1],[1],[1]] => 3
[[4,2,1],[2]] => 2
[[4,2,1],[1,1]] => 2
[[4,1,1,1],[1],[1]] => 3
[[4,1,1,1],[2]] => 2
[[4,1,1,1],[1,1]] => 2
[[3,3,1],[1],[1]] => 3
[[3,3,1],[2]] => 2
[[3,3,1],[1,1]] => 2
[[3,2,2],[1],[1]] => 3
[[3,2,2],[2]] => 2
[[3,2,2],[1,1]] => 2
[[3,2,1,1],[1],[1]] => 3
[[3,2,1,1],[2]] => 2
[[3,2,1,1],[1,1]] => 2
[[3,1,1,1,1],[1],[1]] => 3
[[3,1,1,1,1],[2]] => 2
[[3,1,1,1,1],[1,1]] => 2
[[2,2,2,1],[1],[1]] => 3
[[2,2,2,1],[2]] => 2
[[2,2,2,1],[1,1]] => 2
[[2,2,1,1,1],[1],[1]] => 3
[[2,2,1,1,1],[2]] => 2
[[2,2,1,1,1],[1,1]] => 2
[[2,1,1,1,1,1],[1],[1]] => 3
[[2,1,1,1,1,1],[2]] => 2
[[2,1,1,1,1,1],[1,1]] => 2
[[1,1,1,1,1,1,1],[1],[1]] => 3
[[1,1,1,1,1,1,1],[1,1]] => 2
[[8],[1]] => 2
[[7,1],[1]] => 2
[[6,2],[1]] => 2
[[6,1,1],[1]] => 2
[[5,3],[1]] => 2
[[5,2,1],[1]] => 2
[[5,1,1,1],[1]] => 2
[[4,4],[1]] => 2
[[4,3,1],[1]] => 2
[[4,2,2],[1]] => 2
[[4,2,1,1],[1]] => 2
[[4,1,1,1,1],[1]] => 2
[[3,3,2],[1]] => 2
[[3,3,1,1],[1]] => 2
[[3,2,2,1],[1]] => 2
[[3,2,1,1,1],[1]] => 2
[[3,1,1,1,1,1],[1]] => 2
[[2,2,2,2],[1]] => 2
[[2,2,2,1,1],[1]] => 2
[[2,2,1,1,1,1],[1]] => 2
[[2,1,1,1,1,1,1],[1]] => 2
[[1,1,1,1,1,1,1,1],[1]] => 2
[[9]] => 1
[[8,1]] => 1
[[7,2]] => 1
[[7,1,1]] => 1
[[6,3]] => 1
[[6,2,1]] => 1
[[6,1,1,1]] => 1
[[5,4]] => 1
[[5,3,1]] => 1
[[5,2,2]] => 1
[[5,2,1,1]] => 1
[[5,1,1,1,1]] => 1
[[4,4,1]] => 1
[[4,3,2]] => 1
[[4,3,1,1]] => 1
[[4,2,2,1]] => 1
[[4,2,1,1,1]] => 1
[[4,1,1,1,1,1]] => 1
[[3,3,3]] => 1
[[3,3,2,1]] => 1
[[3,3,1,1,1]] => 1
[[3,2,2,2]] => 1
[[3,2,2,1,1]] => 1
[[3,2,1,1,1,1]] => 1
[[3,1,1,1,1,1,1]] => 1
[[2,2,2,2,1]] => 1
[[2,2,2,1,1,1]] => 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],[1],[1],[1],[1],[1]] => 10
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => 9
[[2],[2],[1],[1],[1],[1],[1],[1]] => 8
[[2],[2],[2],[1],[1],[1],[1]] => 7
[[2],[2],[2],[2],[1],[1]] => 6
[[2],[2],[2],[2],[2]] => 5
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => 9
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => 8
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => 7
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => 6
[[1,1],[1,1],[1,1],[1,1],[1,1]] => 5
[[3],[1],[1],[1],[1],[1],[1],[1]] => 8
[[3],[2],[1],[1],[1],[1],[1]] => 7
[[3],[2],[2],[1],[1],[1]] => 6
[[3],[2],[2],[2],[1]] => 5
[[3],[3],[1],[1],[1],[1]] => 6
[[3],[3],[2],[1],[1]] => 5
[[3],[3],[2],[2]] => 4
[[3],[3],[3],[1]] => 4
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => 8
[[2,1],[2],[1],[1],[1],[1],[1]] => 7
[[2,1],[2],[2],[1],[1],[1]] => 6
[[2,1],[2],[2],[2],[1]] => 5
[[2,1],[1,1],[1],[1],[1],[1],[1]] => 7
[[2,1],[1,1],[1,1],[1],[1],[1]] => 6
[[2,1],[1,1],[1,1],[1,1],[1]] => 5
[[2,1],[2,1],[1],[1],[1],[1]] => 6
[[2,1],[2,1],[2],[1],[1]] => 5
[[2,1],[2,1],[2],[2]] => 4
[[2,1],[2,1],[1,1],[1],[1]] => 5
[[2,1],[2,1],[1,1],[1,1]] => 4
[[2,1],[2,1],[2,1],[1]] => 4
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => 8
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => 7
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => 6
[[1,1,1],[1,1],[1,1],[1,1],[1]] => 5
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => 6
[[1,1,1],[1,1,1],[1,1],[1],[1]] => 5
[[1,1,1],[1,1,1],[1,1],[1,1]] => 4
[[1,1,1],[1,1,1],[1,1,1],[1]] => 4
[[4],[1],[1],[1],[1],[1],[1]] => 7
[[4],[2],[1],[1],[1],[1]] => 6
[[4],[2],[2],[1],[1]] => 5
[[4],[2],[2],[2]] => 4
[[4],[3],[1],[1],[1]] => 5
[[4],[3],[2],[1]] => 4
[[4],[3],[3]] => 3
[[4],[4],[1],[1]] => 4
[[4],[4],[2]] => 3
[[3,1],[1],[1],[1],[1],[1],[1]] => 7
[[3,1],[2],[1],[1],[1],[1]] => 6
[[3,1],[2],[2],[1],[1]] => 5
[[3,1],[2],[2],[2]] => 4
[[3,1],[1,1],[1],[1],[1],[1]] => 6
[[3,1],[1,1],[1,1],[1],[1]] => 5
[[3,1],[1,1],[1,1],[1,1]] => 4
[[3,1],[3],[1],[1],[1]] => 5
[[3,1],[3],[2],[1]] => 4
[[3,1],[3],[3]] => 3
[[3,1],[2,1],[1],[1],[1]] => 5
[[3,1],[2,1],[2],[1]] => 4
[[3,1],[2,1],[1,1],[1]] => 4
[[3,1],[2,1],[2,1]] => 3
[[3,1],[3,1],[1],[1]] => 4
[[3,1],[3,1],[2]] => 3
[[3,1],[3,1],[1,1]] => 3
[[2,2],[1],[1],[1],[1],[1],[1]] => 7
[[2,2],[2],[1],[1],[1],[1]] => 6
[[2,2],[2],[2],[1],[1]] => 5
[[2,2],[2],[2],[2]] => 4
[[2,2],[1,1],[1],[1],[1],[1]] => 6
[[2,2],[1,1],[1,1],[1],[1]] => 5
[[2,2],[1,1],[1,1],[1,1]] => 4
[[2,2],[2,1],[1],[1],[1]] => 5
[[2,2],[2,1],[2],[1]] => 4
[[2,2],[2,1],[1,1],[1]] => 4
[[2,2],[2,1],[2,1]] => 3
[[2,2],[2,2],[1],[1]] => 4
[[2,2],[2,2],[2]] => 3
[[2,2],[2,2],[1,1]] => 3
[[2,1,1],[1],[1],[1],[1],[1],[1]] => 7
[[2,1,1],[2],[1],[1],[1],[1]] => 6
[[2,1,1],[2],[2],[1],[1]] => 5
[[2,1,1],[2],[2],[2]] => 4
[[2,1,1],[1,1],[1],[1],[1],[1]] => 6
[[2,1,1],[1,1],[1,1],[1],[1]] => 5
[[2,1,1],[1,1],[1,1],[1,1]] => 4
[[2,1,1],[2,1],[1],[1],[1]] => 5
[[2,1,1],[2,1],[2],[1]] => 4
[[2,1,1],[2,1],[1,1],[1]] => 4
[[2,1,1],[2,1],[2,1]] => 3
[[2,1,1],[1,1,1],[1],[1],[1]] => 5
[[2,1,1],[1,1,1],[1,1],[1]] => 4
[[2,1,1],[1,1,1],[1,1,1]] => 3
[[2,1,1],[2,1,1],[1],[1]] => 4
[[2,1,1],[2,1,1],[2]] => 3
[[2,1,1],[2,1,1],[1,1]] => 3
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => 7
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => 6
[[1,1,1,1],[1,1],[1,1],[1],[1]] => 5
[[1,1,1,1],[1,1],[1,1],[1,1]] => 4
[[1,1,1,1],[1,1,1],[1],[1],[1]] => 5
[[1,1,1,1],[1,1,1],[1,1],[1]] => 4
[[1,1,1,1],[1,1,1],[1,1,1]] => 3
[[1,1,1,1],[1,1,1,1],[1],[1]] => 4
[[1,1,1,1],[1,1,1,1],[1,1]] => 3
[[5],[1],[1],[1],[1],[1]] => 6
[[5],[2],[1],[1],[1]] => 5
[[5],[2],[2],[1]] => 4
[[5],[3],[1],[1]] => 4
[[5],[3],[2]] => 3
[[5],[4],[1]] => 3
[[5],[5]] => 2
[[4,1],[1],[1],[1],[1],[1]] => 6
[[4,1],[2],[1],[1],[1]] => 5
[[4,1],[2],[2],[1]] => 4
[[4,1],[1,1],[1],[1],[1]] => 5
[[4,1],[1,1],[1,1],[1]] => 4
[[4,1],[3],[1],[1]] => 4
[[4,1],[3],[2]] => 3
[[4,1],[2,1],[1],[1]] => 4
[[4,1],[2,1],[2]] => 3
[[4,1],[2,1],[1,1]] => 3
[[4,1],[4],[1]] => 3
[[4,1],[3,1],[1]] => 3
[[4,1],[4,1]] => 2
[[3,2],[1],[1],[1],[1],[1]] => 6
[[3,2],[2],[1],[1],[1]] => 5
[[3,2],[2],[2],[1]] => 4
[[3,2],[1,1],[1],[1],[1]] => 5
[[3,2],[1,1],[1,1],[1]] => 4
[[3,2],[3],[1],[1]] => 4
[[3,2],[3],[2]] => 3
[[3,2],[2,1],[1],[1]] => 4
[[3,2],[2,1],[2]] => 3
[[3,2],[2,1],[1,1]] => 3
[[3,2],[3,1],[1]] => 3
[[3,2],[2,2],[1]] => 3
[[3,2],[3,2]] => 2
[[3,1,1],[1],[1],[1],[1],[1]] => 6
[[3,1,1],[2],[1],[1],[1]] => 5
[[3,1,1],[2],[2],[1]] => 4
[[3,1,1],[1,1],[1],[1],[1]] => 5
[[3,1,1],[1,1],[1,1],[1]] => 4
[[3,1,1],[3],[1],[1]] => 4
[[3,1,1],[3],[2]] => 3
[[3,1,1],[2,1],[1],[1]] => 4
[[3,1,1],[2,1],[2]] => 3
[[3,1,1],[2,1],[1,1]] => 3
[[3,1,1],[1,1,1],[1],[1]] => 4
[[3,1,1],[1,1,1],[1,1]] => 3
[[3,1,1],[3,1],[1]] => 3
[[3,1,1],[2,1,1],[1]] => 3
[[3,1,1],[3,1,1]] => 2
[[2,2,1],[1],[1],[1],[1],[1]] => 6
[[2,2,1],[2],[1],[1],[1]] => 5
[[2,2,1],[2],[2],[1]] => 4
[[2,2,1],[1,1],[1],[1],[1]] => 5
[[2,2,1],[1,1],[1,1],[1]] => 4
[[2,2,1],[2,1],[1],[1]] => 4
[[2,2,1],[2,1],[2]] => 3
[[2,2,1],[2,1],[1,1]] => 3
[[2,2,1],[1,1,1],[1],[1]] => 4
[[2,2,1],[1,1,1],[1,1]] => 3
[[2,2,1],[2,2],[1]] => 3
[[2,2,1],[2,1,1],[1]] => 3
[[2,2,1],[2,2,1]] => 2
[[2,1,1,1],[1],[1],[1],[1],[1]] => 6
[[2,1,1,1],[2],[1],[1],[1]] => 5
[[2,1,1,1],[2],[2],[1]] => 4
[[2,1,1,1],[1,1],[1],[1],[1]] => 5
[[2,1,1,1],[1,1],[1,1],[1]] => 4
[[2,1,1,1],[2,1],[1],[1]] => 4
[[2,1,1,1],[2,1],[2]] => 3
[[2,1,1,1],[2,1],[1,1]] => 3
[[2,1,1,1],[1,1,1],[1],[1]] => 4
[[2,1,1,1],[1,1,1],[1,1]] => 3
[[2,1,1,1],[2,1,1],[1]] => 3
[[2,1,1,1],[1,1,1,1],[1]] => 3
[[2,1,1,1],[2,1,1,1]] => 2
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => 6
[[1,1,1,1,1],[1,1],[1],[1],[1]] => 5
[[1,1,1,1,1],[1,1],[1,1],[1]] => 4
[[1,1,1,1,1],[1,1,1],[1],[1]] => 4
[[1,1,1,1,1],[1,1,1],[1,1]] => 3
[[1,1,1,1,1],[1,1,1,1],[1]] => 3
[[1,1,1,1,1],[1,1,1,1,1]] => 2
[[6],[1],[1],[1],[1]] => 5
[[6],[2],[1],[1]] => 4
[[6],[2],[2]] => 3
[[6],[3],[1]] => 3
[[6],[4]] => 2
[[5,1],[1],[1],[1],[1]] => 5
[[5,1],[2],[1],[1]] => 4
[[5,1],[2],[2]] => 3
[[5,1],[1,1],[1],[1]] => 4
[[5,1],[1,1],[1,1]] => 3
[[5,1],[3],[1]] => 3
[[5,1],[2,1],[1]] => 3
[[5,1],[4]] => 2
[[5,1],[3,1]] => 2
[[4,2],[1],[1],[1],[1]] => 5
[[4,2],[2],[1],[1]] => 4
[[4,2],[2],[2]] => 3
[[4,2],[1,1],[1],[1]] => 4
[[4,2],[1,1],[1,1]] => 3
[[4,2],[3],[1]] => 3
[[4,2],[2,1],[1]] => 3
[[4,2],[4]] => 2
[[4,2],[3,1]] => 2
[[4,2],[2,2]] => 2
[[4,1,1],[1],[1],[1],[1]] => 5
[[4,1,1],[2],[1],[1]] => 4
[[4,1,1],[2],[2]] => 3
[[4,1,1],[1,1],[1],[1]] => 4
[[4,1,1],[1,1],[1,1]] => 3
[[4,1,1],[3],[1]] => 3
[[4,1,1],[2,1],[1]] => 3
[[4,1,1],[1,1,1],[1]] => 3
[[4,1,1],[4]] => 2
[[4,1,1],[3,1]] => 2
[[4,1,1],[2,1,1]] => 2
[[3,3],[1],[1],[1],[1]] => 5
[[3,3],[2],[1],[1]] => 4
[[3,3],[2],[2]] => 3
[[3,3],[1,1],[1],[1]] => 4
[[3,3],[1,1],[1,1]] => 3
[[3,3],[3],[1]] => 3
[[3,3],[2,1],[1]] => 3
[[3,3],[3,1]] => 2
[[3,3],[2,2]] => 2
[[3,2,1],[1],[1],[1],[1]] => 5
[[3,2,1],[2],[1],[1]] => 4
[[3,2,1],[2],[2]] => 3
[[3,2,1],[1,1],[1],[1]] => 4
[[3,2,1],[1,1],[1,1]] => 3
[[3,2,1],[3],[1]] => 3
[[3,2,1],[2,1],[1]] => 3
[[3,2,1],[1,1,1],[1]] => 3
[[3,2,1],[3,1]] => 2
[[3,2,1],[2,2]] => 2
[[3,2,1],[2,1,1]] => 2
[[3,1,1,1],[1],[1],[1],[1]] => 5
[[3,1,1,1],[2],[1],[1]] => 4
[[3,1,1,1],[2],[2]] => 3
[[3,1,1,1],[1,1],[1],[1]] => 4
[[3,1,1,1],[1,1],[1,1]] => 3
[[3,1,1,1],[3],[1]] => 3
[[3,1,1,1],[2,1],[1]] => 3
[[3,1,1,1],[1,1,1],[1]] => 3
[[3,1,1,1],[3,1]] => 2
[[3,1,1,1],[2,1,1]] => 2
[[3,1,1,1],[1,1,1,1]] => 2
[[2,2,2],[1],[1],[1],[1]] => 5
[[2,2,2],[2],[1],[1]] => 4
[[2,2,2],[2],[2]] => 3
[[2,2,2],[1,1],[1],[1]] => 4
[[2,2,2],[1,1],[1,1]] => 3
[[2,2,2],[2,1],[1]] => 3
[[2,2,2],[1,1,1],[1]] => 3
[[2,2,2],[2,2]] => 2
[[2,2,2],[2,1,1]] => 2
[[2,2,1,1],[1],[1],[1],[1]] => 5
[[2,2,1,1],[2],[1],[1]] => 4
[[2,2,1,1],[2],[2]] => 3
[[2,2,1,1],[1,1],[1],[1]] => 4
[[2,2,1,1],[1,1],[1,1]] => 3
[[2,2,1,1],[2,1],[1]] => 3
[[2,2,1,1],[1,1,1],[1]] => 3
[[2,2,1,1],[2,2]] => 2
[[2,2,1,1],[2,1,1]] => 2
[[2,2,1,1],[1,1,1,1]] => 2
[[2,1,1,1,1],[1],[1],[1],[1]] => 5
[[2,1,1,1,1],[2],[1],[1]] => 4
[[2,1,1,1,1],[2],[2]] => 3
[[2,1,1,1,1],[1,1],[1],[1]] => 4
[[2,1,1,1,1],[1,1],[1,1]] => 3
[[2,1,1,1,1],[2,1],[1]] => 3
[[2,1,1,1,1],[1,1,1],[1]] => 3
[[2,1,1,1,1],[2,1,1]] => 2
[[2,1,1,1,1],[1,1,1,1]] => 2
[[1,1,1,1,1,1],[1],[1],[1],[1]] => 5
[[1,1,1,1,1,1],[1,1],[1],[1]] => 4
[[1,1,1,1,1,1],[1,1],[1,1]] => 3
[[1,1,1,1,1,1],[1,1,1],[1]] => 3
[[1,1,1,1,1,1],[1,1,1,1]] => 2
[[7],[1],[1],[1]] => 4
[[7],[2],[1]] => 3
[[7],[3]] => 2
[[6,1],[1],[1],[1]] => 4
[[6,1],[2],[1]] => 3
[[6,1],[1,1],[1]] => 3
[[6,1],[3]] => 2
[[6,1],[2,1]] => 2
[[5,2],[1],[1],[1]] => 4
[[5,2],[2],[1]] => 3
[[5,2],[1,1],[1]] => 3
[[5,2],[3]] => 2
[[5,2],[2,1]] => 2
[[5,1,1],[1],[1],[1]] => 4
[[5,1,1],[2],[1]] => 3
[[5,1,1],[1,1],[1]] => 3
[[5,1,1],[3]] => 2
[[5,1,1],[2,1]] => 2
[[5,1,1],[1,1,1]] => 2
[[4,3],[1],[1],[1]] => 4
[[4,3],[2],[1]] => 3
[[4,3],[1,1],[1]] => 3
[[4,3],[3]] => 2
[[4,3],[2,1]] => 2
[[4,2,1],[1],[1],[1]] => 4
[[4,2,1],[2],[1]] => 3
[[4,2,1],[1,1],[1]] => 3
[[4,2,1],[3]] => 2
[[4,2,1],[2,1]] => 2
[[4,2,1],[1,1,1]] => 2
[[4,1,1,1],[1],[1],[1]] => 4
[[4,1,1,1],[2],[1]] => 3
[[4,1,1,1],[1,1],[1]] => 3
[[4,1,1,1],[3]] => 2
[[4,1,1,1],[2,1]] => 2
[[4,1,1,1],[1,1,1]] => 2
[[3,3,1],[1],[1],[1]] => 4
[[3,3,1],[2],[1]] => 3
[[3,3,1],[1,1],[1]] => 3
[[3,3,1],[3]] => 2
[[3,3,1],[2,1]] => 2
[[3,3,1],[1,1,1]] => 2
[[3,2,2],[1],[1],[1]] => 4
[[3,2,2],[2],[1]] => 3
[[3,2,2],[1,1],[1]] => 3
[[3,2,2],[3]] => 2
[[3,2,2],[2,1]] => 2
[[3,2,2],[1,1,1]] => 2
[[3,2,1,1],[1],[1],[1]] => 4
[[3,2,1,1],[2],[1]] => 3
[[3,2,1,1],[1,1],[1]] => 3
[[3,2,1,1],[3]] => 2
[[3,2,1,1],[2,1]] => 2
[[3,2,1,1],[1,1,1]] => 2
[[3,1,1,1,1],[1],[1],[1]] => 4
[[3,1,1,1,1],[2],[1]] => 3
[[3,1,1,1,1],[1,1],[1]] => 3
[[3,1,1,1,1],[3]] => 2
[[3,1,1,1,1],[2,1]] => 2
[[3,1,1,1,1],[1,1,1]] => 2
[[2,2,2,1],[1],[1],[1]] => 4
[[2,2,2,1],[2],[1]] => 3
[[2,2,2,1],[1,1],[1]] => 3
[[2,2,2,1],[2,1]] => 2
[[2,2,2,1],[1,1,1]] => 2
[[2,2,1,1,1],[1],[1],[1]] => 4
[[2,2,1,1,1],[2],[1]] => 3
[[2,2,1,1,1],[1,1],[1]] => 3
[[2,2,1,1,1],[2,1]] => 2
[[2,2,1,1,1],[1,1,1]] => 2
[[2,1,1,1,1,1],[1],[1],[1]] => 4
[[2,1,1,1,1,1],[2],[1]] => 3
[[2,1,1,1,1,1],[1,1],[1]] => 3
[[2,1,1,1,1,1],[2,1]] => 2
[[2,1,1,1,1,1],[1,1,1]] => 2
[[1,1,1,1,1,1,1],[1],[1],[1]] => 4
[[1,1,1,1,1,1,1],[1,1],[1]] => 3
[[1,1,1,1,1,1,1],[1,1,1]] => 2
[[8],[1],[1]] => 3
[[8],[2]] => 2
[[7,1],[1],[1]] => 3
[[7,1],[2]] => 2
[[7,1],[1,1]] => 2
[[6,2],[1],[1]] => 3
[[6,2],[2]] => 2
[[6,2],[1,1]] => 2
[[6,1,1],[1],[1]] => 3
[[6,1,1],[2]] => 2
[[6,1,1],[1,1]] => 2
[[5,3],[1],[1]] => 3
[[5,3],[2]] => 2
[[5,3],[1,1]] => 2
[[5,2,1],[1],[1]] => 3
[[5,2,1],[2]] => 2
[[5,2,1],[1,1]] => 2
[[5,1,1,1],[1],[1]] => 3
[[5,1,1,1],[2]] => 2
[[5,1,1,1],[1,1]] => 2
[[4,4],[1],[1]] => 3
[[4,4],[2]] => 2
[[4,4],[1,1]] => 2
[[4,3,1],[1],[1]] => 3
[[4,3,1],[2]] => 2
[[4,3,1],[1,1]] => 2
[[4,2,2],[1],[1]] => 3
[[4,2,2],[2]] => 2
[[4,2,2],[1,1]] => 2
[[4,2,1,1],[1],[1]] => 3
[[4,2,1,1],[2]] => 2
[[4,2,1,1],[1,1]] => 2
[[4,1,1,1,1],[1],[1]] => 3
[[4,1,1,1,1],[2]] => 2
[[4,1,1,1,1],[1,1]] => 2
[[3,3,2],[1],[1]] => 3
[[3,3,2],[2]] => 2
[[3,3,2],[1,1]] => 2
[[3,3,1,1],[1],[1]] => 3
[[3,3,1,1],[2]] => 2
[[3,3,1,1],[1,1]] => 2
[[3,2,2,1],[1],[1]] => 3
[[3,2,2,1],[2]] => 2
[[3,2,2,1],[1,1]] => 2
[[3,2,1,1,1],[1],[1]] => 3
[[3,2,1,1,1],[2]] => 2
[[3,2,1,1,1],[1,1]] => 2
[[3,1,1,1,1,1],[1],[1]] => 3
[[3,1,1,1,1,1],[2]] => 2
[[3,1,1,1,1,1],[1,1]] => 2
[[2,2,2,2],[1],[1]] => 3
[[2,2,2,2],[2]] => 2
[[2,2,2,2],[1,1]] => 2
[[2,2,2,1,1],[1],[1]] => 3
[[2,2,2,1,1],[2]] => 2
[[2,2,2,1,1],[1,1]] => 2
[[2,2,1,1,1,1],[1],[1]] => 3
[[2,2,1,1,1,1],[2]] => 2
[[2,2,1,1,1,1],[1,1]] => 2
[[2,1,1,1,1,1,1],[1],[1]] => 3
[[2,1,1,1,1,1,1],[2]] => 2
[[2,1,1,1,1,1,1],[1,1]] => 2
[[1,1,1,1,1,1,1,1],[1],[1]] => 3
[[1,1,1,1,1,1,1,1],[1,1]] => 2
[[9],[1]] => 2
[[8,1],[1]] => 2
[[7,2],[1]] => 2
[[7,1,1],[1]] => 2
[[6,3],[1]] => 2
[[6,2,1],[1]] => 2
[[6,1,1,1],[1]] => 2
[[5,4],[1]] => 2
[[5,3,1],[1]] => 2
[[5,2,2],[1]] => 2
[[5,2,1,1],[1]] => 2
[[5,1,1,1,1],[1]] => 2
[[4,4,1],[1]] => 2
[[4,3,2],[1]] => 2
[[4,3,1,1],[1]] => 2
[[4,2,2,1],[1]] => 2
[[4,2,1,1,1],[1]] => 2
[[4,1,1,1,1,1],[1]] => 2
[[3,3,3],[1]] => 2
[[3,3,2,1],[1]] => 2
[[3,3,1,1,1],[1]] => 2
[[3,2,2,2],[1]] => 2
[[3,2,2,1,1],[1]] => 2
[[3,2,1,1,1,1],[1]] => 2
[[3,1,1,1,1,1,1],[1]] => 2
[[2,2,2,2,1],[1]] => 2
[[2,2,2,1,1,1],[1]] => 2
[[2,2,1,1,1,1,1],[1]] => 2
[[2,1,1,1,1,1,1,1],[1]] => 2
[[1,1,1,1,1,1,1,1,1],[1]] => 2
[[10]] => 1
[[9,1]] => 1
[[8,2]] => 1
[[8,1,1]] => 1
[[7,3]] => 1
[[7,2,1]] => 1
[[7,1,1,1]] => 1
[[6,4]] => 1
[[6,3,1]] => 1
[[6,2,2]] => 1
[[6,2,1,1]] => 1
[[6,1,1,1,1]] => 1
[[5,5]] => 1
[[5,4,1]] => 1
[[5,3,2]] => 1
[[5,3,1,1]] => 1
[[5,2,2,1]] => 1
[[5,2,1,1,1]] => 1
[[5,1,1,1,1,1]] => 1
[[4,4,2]] => 1
[[4,4,1,1]] => 1
[[4,3,3]] => 1
[[4,3,2,1]] => 1
[[4,3,1,1,1]] => 1
[[4,2,2,2]] => 1
[[4,2,2,1,1]] => 1
[[4,2,1,1,1,1]] => 1
[[4,1,1,1,1,1,1]] => 1
[[3,3,3,1]] => 1
[[3,3,2,2]] => 1
[[3,3,2,1,1]] => 1
[[3,3,1,1,1,1]] => 1
[[3,2,2,2,1]] => 1
[[3,2,2,1,1,1]] => 1
[[3,2,1,1,1,1,1]] => 1
[[3,1,1,1,1,1,1,1]] => 1
[[2,2,2,2,2]] => 1
[[2,2,2,2,1,1]] => 1
[[2,2,2,1,1,1,1]] => 1
[[2,2,1,1,1,1,1,1]] => 1
[[2,1,1,1,1,1,1,1,1]] => 1
[[1,1,1,1,1,1,1,1,1,1]] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 3,2,1 5,5,2,1 7,9,5,2,1 11,18,11,5,2,1 15,30,22,11,5,2,1 22,53,42,24,11,5,2,1 30,85,78,46,24,11,5,2,1 42,139,138,90,48,24,11,5,2,1
$F_{1} = q$
$F_{2} = 2\ q + q^{2}$
$F_{3} = 3\ q + 2\ q^{2} + q^{3}$
$F_{4} = 5\ q + 5\ q^{2} + 2\ q^{3} + q^{4}$
$F_{5} = 7\ q + 9\ q^{2} + 5\ q^{3} + 2\ q^{4} + q^{5}$
$F_{6} = 11\ q + 18\ q^{2} + 11\ q^{3} + 5\ q^{4} + 2\ q^{5} + q^{6}$
$F_{7} = 15\ q + 30\ q^{2} + 22\ q^{3} + 11\ q^{4} + 5\ q^{5} + 2\ q^{6} + q^{7}$
$F_{8} = 22\ q + 53\ q^{2} + 42\ q^{3} + 24\ q^{4} + 11\ q^{5} + 5\ q^{6} + 2\ q^{7} + q^{8}$
$F_{9} = 30\ q + 85\ q^{2} + 78\ q^{3} + 46\ q^{4} + 24\ q^{5} + 11\ q^{6} + 5\ q^{7} + 2\ q^{8} + q^{9}$
$F_{10} = 42\ q + 139\ q^{2} + 138\ q^{3} + 90\ q^{4} + 48\ q^{5} + 24\ q^{6} + 11\ q^{7} + 5\ q^{8} + 2\ q^{9} + q^{10}$
Description
Number of rows in the plane partition.
Code
def statistic(PP):
return len(list(PP))
Created
Jul 25, 2019 at 23:30 by Erika Pirnes
Updated
Jul 26, 2019 at 13:59 by Christian Stump
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