Identifier
- St001452: Plane partitions ⟶ ℤ
Values
[[1]] => 0
[[1],[1]] => 0
[[2]] => 1
[[1,1]] => 0
[[1],[1],[1]] => 0
[[2],[1]] => 1
[[1,1],[1]] => 0
[[3]] => 0
[[2,1]] => 1
[[1,1,1]] => 0
[[1],[1],[1],[1]] => 0
[[2],[1],[1]] => 1
[[2],[2]] => 2
[[1,1],[1],[1]] => 0
[[1,1],[1,1]] => 0
[[3],[1]] => 0
[[2,1],[1]] => 1
[[1,1,1],[1]] => 0
[[4]] => 1
[[3,1]] => 0
[[2,2]] => 2
[[2,1,1]] => 1
[[1,1,1,1]] => 0
[[1],[1],[1],[1],[1]] => 0
[[2],[1],[1],[1]] => 1
[[2],[2],[1]] => 2
[[1,1],[1],[1],[1]] => 0
[[1,1],[1,1],[1]] => 0
[[3],[1],[1]] => 0
[[3],[2]] => 1
[[2,1],[1],[1]] => 1
[[2,1],[2]] => 2
[[2,1],[1,1]] => 1
[[1,1,1],[1],[1]] => 0
[[1,1,1],[1,1]] => 0
[[4],[1]] => 1
[[3,1],[1]] => 0
[[2,2],[1]] => 2
[[2,1,1],[1]] => 1
[[1,1,1,1],[1]] => 0
[[5]] => 0
[[4,1]] => 1
[[3,2]] => 1
[[3,1,1]] => 0
[[2,2,1]] => 2
[[2,1,1,1]] => 1
[[1,1,1,1,1]] => 0
[[1],[1],[1],[1],[1],[1]] => 0
[[2],[1],[1],[1],[1]] => 1
[[2],[2],[1],[1]] => 2
[[2],[2],[2]] => 3
[[1,1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1],[1]] => 0
[[1,1],[1,1],[1,1]] => 0
[[3],[1],[1],[1]] => 0
[[3],[2],[1]] => 1
[[3],[3]] => 0
[[2,1],[1],[1],[1]] => 1
[[2,1],[2],[1]] => 2
[[2,1],[1,1],[1]] => 1
[[2,1],[2,1]] => 2
[[1,1,1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1]] => 0
[[1,1,1],[1,1,1]] => 0
[[4],[1],[1]] => 1
[[4],[2]] => 2
[[3,1],[1],[1]] => 0
[[3,1],[2]] => 1
[[3,1],[1,1]] => 0
[[2,2],[1],[1]] => 2
[[2,2],[2]] => 3
[[2,2],[1,1]] => 2
[[2,1,1],[1],[1]] => 1
[[2,1,1],[2]] => 2
[[2,1,1],[1,1]] => 1
[[1,1,1,1],[1],[1]] => 0
[[1,1,1,1],[1,1]] => 0
[[5],[1]] => 0
[[4,1],[1]] => 1
[[3,2],[1]] => 1
[[3,1,1],[1]] => 0
[[2,2,1],[1]] => 2
[[2,1,1,1],[1]] => 1
[[1,1,1,1,1],[1]] => 0
[[6]] => 1
[[5,1]] => 0
[[4,2]] => 2
[[4,1,1]] => 1
[[3,3]] => 0
[[3,2,1]] => 1
[[3,1,1,1]] => 0
[[2,2,2]] => 3
[[2,2,1,1]] => 2
[[2,1,1,1,1]] => 1
[[1,1,1,1,1,1]] => 0
[[1],[1],[1],[1],[1],[1],[1]] => 0
[[2],[1],[1],[1],[1],[1]] => 1
[[2],[2],[1],[1],[1]] => 2
[[2],[2],[2],[1]] => 3
[[1,1],[1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1],[1],[1]] => 0
>>> Load all 1123 entries. <<<[[1,1],[1,1],[1,1],[1]] => 0
[[3],[1],[1],[1],[1]] => 0
[[3],[2],[1],[1]] => 1
[[3],[2],[2]] => 2
[[3],[3],[1]] => 0
[[2,1],[1],[1],[1],[1]] => 1
[[2,1],[2],[1],[1]] => 2
[[2,1],[2],[2]] => 3
[[2,1],[1,1],[1],[1]] => 1
[[2,1],[1,1],[1,1]] => 1
[[2,1],[2,1],[1]] => 2
[[1,1,1],[1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1],[1]] => 0
[[1,1,1],[1,1],[1,1]] => 0
[[1,1,1],[1,1,1],[1]] => 0
[[4],[1],[1],[1]] => 1
[[4],[2],[1]] => 2
[[4],[3]] => 1
[[3,1],[1],[1],[1]] => 0
[[3,1],[2],[1]] => 1
[[3,1],[1,1],[1]] => 0
[[3,1],[3]] => 0
[[3,1],[2,1]] => 1
[[2,2],[1],[1],[1]] => 2
[[2,2],[2],[1]] => 3
[[2,2],[1,1],[1]] => 2
[[2,2],[2,1]] => 3
[[2,1,1],[1],[1],[1]] => 1
[[2,1,1],[2],[1]] => 2
[[2,1,1],[1,1],[1]] => 1
[[2,1,1],[2,1]] => 2
[[2,1,1],[1,1,1]] => 1
[[1,1,1,1],[1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1]] => 0
[[1,1,1,1],[1,1,1]] => 0
[[5],[1],[1]] => 0
[[5],[2]] => 1
[[4,1],[1],[1]] => 1
[[4,1],[2]] => 2
[[4,1],[1,1]] => 1
[[3,2],[1],[1]] => 1
[[3,2],[2]] => 2
[[3,2],[1,1]] => 1
[[3,1,1],[1],[1]] => 0
[[3,1,1],[2]] => 1
[[3,1,1],[1,1]] => 0
[[2,2,1],[1],[1]] => 2
[[2,2,1],[2]] => 3
[[2,2,1],[1,1]] => 2
[[2,1,1,1],[1],[1]] => 1
[[2,1,1,1],[2]] => 2
[[2,1,1,1],[1,1]] => 1
[[1,1,1,1,1],[1],[1]] => 0
[[1,1,1,1,1],[1,1]] => 0
[[6],[1]] => 1
[[5,1],[1]] => 0
[[4,2],[1]] => 2
[[4,1,1],[1]] => 1
[[3,3],[1]] => 0
[[3,2,1],[1]] => 1
[[3,1,1,1],[1]] => 0
[[2,2,2],[1]] => 3
[[2,2,1,1],[1]] => 2
[[2,1,1,1,1],[1]] => 1
[[1,1,1,1,1,1],[1]] => 0
[[7]] => 0
[[6,1]] => 1
[[5,2]] => 1
[[5,1,1]] => 0
[[4,3]] => 1
[[4,2,1]] => 2
[[4,1,1,1]] => 1
[[3,3,1]] => 0
[[3,2,2]] => 2
[[3,2,1,1]] => 1
[[3,1,1,1,1]] => 0
[[2,2,2,1]] => 3
[[2,2,1,1,1]] => 2
[[2,1,1,1,1,1]] => 1
[[1,1,1,1,1,1,1]] => 0
[[1],[1],[1],[1],[1],[1],[1],[1]] => 0
[[2],[1],[1],[1],[1],[1],[1]] => 1
[[2],[2],[1],[1],[1],[1]] => 2
[[2],[2],[2],[1],[1]] => 3
[[2],[2],[2],[2]] => 4
[[1,1],[1],[1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1,1],[1],[1]] => 0
[[1,1],[1,1],[1,1],[1,1]] => 0
[[3],[1],[1],[1],[1],[1]] => 0
[[3],[2],[1],[1],[1]] => 1
[[3],[2],[2],[1]] => 2
[[3],[3],[1],[1]] => 0
[[3],[3],[2]] => 1
[[2,1],[1],[1],[1],[1],[1]] => 1
[[2,1],[2],[1],[1],[1]] => 2
[[2,1],[2],[2],[1]] => 3
[[2,1],[1,1],[1],[1],[1]] => 1
[[2,1],[1,1],[1,1],[1]] => 1
[[2,1],[2,1],[1],[1]] => 2
[[2,1],[2,1],[2]] => 3
[[2,1],[2,1],[1,1]] => 2
[[1,1,1],[1],[1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1,1],[1]] => 0
[[1,1,1],[1,1,1],[1],[1]] => 0
[[1,1,1],[1,1,1],[1,1]] => 0
[[4],[1],[1],[1],[1]] => 1
[[4],[2],[1],[1]] => 2
[[4],[2],[2]] => 3
[[4],[3],[1]] => 1
[[4],[4]] => 2
[[3,1],[1],[1],[1],[1]] => 0
[[3,1],[2],[1],[1]] => 1
[[3,1],[2],[2]] => 2
[[3,1],[1,1],[1],[1]] => 0
[[3,1],[1,1],[1,1]] => 0
[[3,1],[3],[1]] => 0
[[3,1],[2,1],[1]] => 1
[[3,1],[3,1]] => 0
[[2,2],[1],[1],[1],[1]] => 2
[[2,2],[2],[1],[1]] => 3
[[2,2],[2],[2]] => 4
[[2,2],[1,1],[1],[1]] => 2
[[2,2],[1,1],[1,1]] => 2
[[2,2],[2,1],[1]] => 3
[[2,2],[2,2]] => 4
[[2,1,1],[1],[1],[1],[1]] => 1
[[2,1,1],[2],[1],[1]] => 2
[[2,1,1],[2],[2]] => 3
[[2,1,1],[1,1],[1],[1]] => 1
[[2,1,1],[1,1],[1,1]] => 1
[[2,1,1],[2,1],[1]] => 2
[[2,1,1],[1,1,1],[1]] => 1
[[2,1,1],[2,1,1]] => 2
[[1,1,1,1],[1],[1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1,1]] => 0
[[1,1,1,1],[1,1,1],[1]] => 0
[[1,1,1,1],[1,1,1,1]] => 0
[[5],[1],[1],[1]] => 0
[[5],[2],[1]] => 1
[[5],[3]] => 0
[[4,1],[1],[1],[1]] => 1
[[4,1],[2],[1]] => 2
[[4,1],[1,1],[1]] => 1
[[4,1],[3]] => 1
[[4,1],[2,1]] => 2
[[3,2],[1],[1],[1]] => 1
[[3,2],[2],[1]] => 2
[[3,2],[1,1],[1]] => 1
[[3,2],[3]] => 1
[[3,2],[2,1]] => 2
[[3,1,1],[1],[1],[1]] => 0
[[3,1,1],[2],[1]] => 1
[[3,1,1],[1,1],[1]] => 0
[[3,1,1],[3]] => 0
[[3,1,1],[2,1]] => 1
[[3,1,1],[1,1,1]] => 0
[[2,2,1],[1],[1],[1]] => 2
[[2,2,1],[2],[1]] => 3
[[2,2,1],[1,1],[1]] => 2
[[2,2,1],[2,1]] => 3
[[2,2,1],[1,1,1]] => 2
[[2,1,1,1],[1],[1],[1]] => 1
[[2,1,1,1],[2],[1]] => 2
[[2,1,1,1],[1,1],[1]] => 1
[[2,1,1,1],[2,1]] => 2
[[2,1,1,1],[1,1,1]] => 1
[[1,1,1,1,1],[1],[1],[1]] => 0
[[1,1,1,1,1],[1,1],[1]] => 0
[[1,1,1,1,1],[1,1,1]] => 0
[[6],[1],[1]] => 1
[[6],[2]] => 2
[[5,1],[1],[1]] => 0
[[5,1],[2]] => 1
[[5,1],[1,1]] => 0
[[4,2],[1],[1]] => 2
[[4,2],[2]] => 3
[[4,2],[1,1]] => 2
[[4,1,1],[1],[1]] => 1
[[4,1,1],[2]] => 2
[[4,1,1],[1,1]] => 1
[[3,3],[1],[1]] => 0
[[3,3],[2]] => 1
[[3,3],[1,1]] => 0
[[3,2,1],[1],[1]] => 1
[[3,2,1],[2]] => 2
[[3,2,1],[1,1]] => 1
[[3,1,1,1],[1],[1]] => 0
[[3,1,1,1],[2]] => 1
[[3,1,1,1],[1,1]] => 0
[[2,2,2],[1],[1]] => 3
[[2,2,2],[2]] => 4
[[2,2,2],[1,1]] => 3
[[2,2,1,1],[1],[1]] => 2
[[2,2,1,1],[2]] => 3
[[2,2,1,1],[1,1]] => 2
[[2,1,1,1,1],[1],[1]] => 1
[[2,1,1,1,1],[2]] => 2
[[2,1,1,1,1],[1,1]] => 1
[[1,1,1,1,1,1],[1],[1]] => 0
[[1,1,1,1,1,1],[1,1]] => 0
[[7],[1]] => 0
[[6,1],[1]] => 1
[[5,2],[1]] => 1
[[5,1,1],[1]] => 0
[[4,3],[1]] => 1
[[4,2,1],[1]] => 2
[[4,1,1,1],[1]] => 1
[[3,3,1],[1]] => 0
[[3,2,2],[1]] => 2
[[3,2,1,1],[1]] => 1
[[3,1,1,1,1],[1]] => 0
[[2,2,2,1],[1]] => 3
[[2,2,1,1,1],[1]] => 2
[[2,1,1,1,1,1],[1]] => 1
[[1,1,1,1,1,1,1],[1]] => 0
[[8]] => 1
[[7,1]] => 0
[[6,2]] => 2
[[6,1,1]] => 1
[[5,3]] => 0
[[5,2,1]] => 1
[[5,1,1,1]] => 0
[[4,4]] => 2
[[4,3,1]] => 1
[[4,2,2]] => 3
[[4,2,1,1]] => 2
[[4,1,1,1,1]] => 1
[[3,3,2]] => 1
[[3,3,1,1]] => 0
[[3,2,2,1]] => 2
[[3,2,1,1,1]] => 1
[[3,1,1,1,1,1]] => 0
[[2,2,2,2]] => 4
[[2,2,2,1,1]] => 3
[[2,2,1,1,1,1]] => 2
[[2,1,1,1,1,1,1]] => 1
[[1,1,1,1,1,1,1,1]] => 0
[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => 0
[[2],[1],[1],[1],[1],[1],[1],[1]] => 1
[[2],[2],[1],[1],[1],[1],[1]] => 2
[[2],[2],[2],[1],[1],[1]] => 3
[[2],[2],[2],[2],[1]] => 4
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1,1],[1],[1],[1]] => 0
[[1,1],[1,1],[1,1],[1,1],[1]] => 0
[[3],[1],[1],[1],[1],[1],[1]] => 0
[[3],[2],[1],[1],[1],[1]] => 1
[[3],[2],[2],[1],[1]] => 2
[[3],[2],[2],[2]] => 3
[[3],[3],[1],[1],[1]] => 0
[[3],[3],[2],[1]] => 1
[[3],[3],[3]] => 0
[[2,1],[1],[1],[1],[1],[1],[1]] => 1
[[2,1],[2],[1],[1],[1],[1]] => 2
[[2,1],[2],[2],[1],[1]] => 3
[[2,1],[2],[2],[2]] => 4
[[2,1],[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
[[2,1],[2,1],[1],[1],[1]] => 2
[[2,1],[2,1],[2],[1]] => 3
[[2,1],[2,1],[1,1],[1]] => 2
[[2,1],[2,1],[2,1]] => 3
[[1,1,1],[1],[1],[1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1,1],[1],[1]] => 0
[[1,1,1],[1,1],[1,1],[1,1]] => 0
[[1,1,1],[1,1,1],[1],[1],[1]] => 0
[[1,1,1],[1,1,1],[1,1],[1]] => 0
[[1,1,1],[1,1,1],[1,1,1]] => 0
[[4],[1],[1],[1],[1],[1]] => 1
[[4],[2],[1],[1],[1]] => 2
[[4],[2],[2],[1]] => 3
[[4],[3],[1],[1]] => 1
[[4],[3],[2]] => 2
[[4],[4],[1]] => 2
[[3,1],[1],[1],[1],[1],[1]] => 0
[[3,1],[2],[1],[1],[1]] => 1
[[3,1],[2],[2],[1]] => 2
[[3,1],[1,1],[1],[1],[1]] => 0
[[3,1],[1,1],[1,1],[1]] => 0
[[3,1],[3],[1],[1]] => 0
[[3,1],[3],[2]] => 1
[[3,1],[2,1],[1],[1]] => 1
[[3,1],[2,1],[2]] => 2
[[3,1],[2,1],[1,1]] => 1
[[3,1],[3,1],[1]] => 0
[[2,2],[1],[1],[1],[1],[1]] => 2
[[2,2],[2],[1],[1],[1]] => 3
[[2,2],[2],[2],[1]] => 4
[[2,2],[1,1],[1],[1],[1]] => 2
[[2,2],[1,1],[1,1],[1]] => 2
[[2,2],[2,1],[1],[1]] => 3
[[2,2],[2,1],[2]] => 4
[[2,2],[2,1],[1,1]] => 3
[[2,2],[2,2],[1]] => 4
[[2,1,1],[1],[1],[1],[1],[1]] => 1
[[2,1,1],[2],[1],[1],[1]] => 2
[[2,1,1],[2],[2],[1]] => 3
[[2,1,1],[1,1],[1],[1],[1]] => 1
[[2,1,1],[1,1],[1,1],[1]] => 1
[[2,1,1],[2,1],[1],[1]] => 2
[[2,1,1],[2,1],[2]] => 3
[[2,1,1],[2,1],[1,1]] => 2
[[2,1,1],[1,1,1],[1],[1]] => 1
[[2,1,1],[1,1,1],[1,1]] => 1
[[2,1,1],[2,1,1],[1]] => 2
[[1,1,1,1],[1],[1],[1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1,1],[1]] => 0
[[1,1,1,1],[1,1,1],[1],[1]] => 0
[[1,1,1,1],[1,1,1],[1,1]] => 0
[[1,1,1,1],[1,1,1,1],[1]] => 0
[[5],[1],[1],[1],[1]] => 0
[[5],[2],[1],[1]] => 1
[[5],[2],[2]] => 2
[[5],[3],[1]] => 0
[[5],[4]] => 1
[[4,1],[1],[1],[1],[1]] => 1
[[4,1],[2],[1],[1]] => 2
[[4,1],[2],[2]] => 3
[[4,1],[1,1],[1],[1]] => 1
[[4,1],[1,1],[1,1]] => 1
[[4,1],[3],[1]] => 1
[[4,1],[2,1],[1]] => 2
[[4,1],[4]] => 2
[[4,1],[3,1]] => 1
[[3,2],[1],[1],[1],[1]] => 1
[[3,2],[2],[1],[1]] => 2
[[3,2],[2],[2]] => 3
[[3,2],[1,1],[1],[1]] => 1
[[3,2],[1,1],[1,1]] => 1
[[3,2],[3],[1]] => 1
[[3,2],[2,1],[1]] => 2
[[3,2],[3,1]] => 1
[[3,2],[2,2]] => 3
[[3,1,1],[1],[1],[1],[1]] => 0
[[3,1,1],[2],[1],[1]] => 1
[[3,1,1],[2],[2]] => 2
[[3,1,1],[1,1],[1],[1]] => 0
[[3,1,1],[1,1],[1,1]] => 0
[[3,1,1],[3],[1]] => 0
[[3,1,1],[2,1],[1]] => 1
[[3,1,1],[1,1,1],[1]] => 0
[[3,1,1],[3,1]] => 0
[[3,1,1],[2,1,1]] => 1
[[2,2,1],[1],[1],[1],[1]] => 2
[[2,2,1],[2],[1],[1]] => 3
[[2,2,1],[2],[2]] => 4
[[2,2,1],[1,1],[1],[1]] => 2
[[2,2,1],[1,1],[1,1]] => 2
[[2,2,1],[2,1],[1]] => 3
[[2,2,1],[1,1,1],[1]] => 2
[[2,2,1],[2,2]] => 4
[[2,2,1],[2,1,1]] => 3
[[2,1,1,1],[1],[1],[1],[1]] => 1
[[2,1,1,1],[2],[1],[1]] => 2
[[2,1,1,1],[2],[2]] => 3
[[2,1,1,1],[1,1],[1],[1]] => 1
[[2,1,1,1],[1,1],[1,1]] => 1
[[2,1,1,1],[2,1],[1]] => 2
[[2,1,1,1],[1,1,1],[1]] => 1
[[2,1,1,1],[2,1,1]] => 2
[[2,1,1,1],[1,1,1,1]] => 1
[[1,1,1,1,1],[1],[1],[1],[1]] => 0
[[1,1,1,1,1],[1,1],[1],[1]] => 0
[[1,1,1,1,1],[1,1],[1,1]] => 0
[[1,1,1,1,1],[1,1,1],[1]] => 0
[[1,1,1,1,1],[1,1,1,1]] => 0
[[6],[1],[1],[1]] => 1
[[6],[2],[1]] => 2
[[6],[3]] => 1
[[5,1],[1],[1],[1]] => 0
[[5,1],[2],[1]] => 1
[[5,1],[1,1],[1]] => 0
[[5,1],[3]] => 0
[[5,1],[2,1]] => 1
[[4,2],[1],[1],[1]] => 2
[[4,2],[2],[1]] => 3
[[4,2],[1,1],[1]] => 2
[[4,2],[3]] => 2
[[4,2],[2,1]] => 3
[[4,1,1],[1],[1],[1]] => 1
[[4,1,1],[2],[1]] => 2
[[4,1,1],[1,1],[1]] => 1
[[4,1,1],[3]] => 1
[[4,1,1],[2,1]] => 2
[[4,1,1],[1,1,1]] => 1
[[3,3],[1],[1],[1]] => 0
[[3,3],[2],[1]] => 1
[[3,3],[1,1],[1]] => 0
[[3,3],[3]] => 0
[[3,3],[2,1]] => 1
[[3,2,1],[1],[1],[1]] => 1
[[3,2,1],[2],[1]] => 2
[[3,2,1],[1,1],[1]] => 1
[[3,2,1],[3]] => 1
[[3,2,1],[2,1]] => 2
[[3,2,1],[1,1,1]] => 1
[[3,1,1,1],[1],[1],[1]] => 0
[[3,1,1,1],[2],[1]] => 1
[[3,1,1,1],[1,1],[1]] => 0
[[3,1,1,1],[3]] => 0
[[3,1,1,1],[2,1]] => 1
[[3,1,1,1],[1,1,1]] => 0
[[2,2,2],[1],[1],[1]] => 3
[[2,2,2],[2],[1]] => 4
[[2,2,2],[1,1],[1]] => 3
[[2,2,2],[2,1]] => 4
[[2,2,2],[1,1,1]] => 3
[[2,2,1,1],[1],[1],[1]] => 2
[[2,2,1,1],[2],[1]] => 3
[[2,2,1,1],[1,1],[1]] => 2
[[2,2,1,1],[2,1]] => 3
[[2,2,1,1],[1,1,1]] => 2
[[2,1,1,1,1],[1],[1],[1]] => 1
[[2,1,1,1,1],[2],[1]] => 2
[[2,1,1,1,1],[1,1],[1]] => 1
[[2,1,1,1,1],[2,1]] => 2
[[2,1,1,1,1],[1,1,1]] => 1
[[1,1,1,1,1,1],[1],[1],[1]] => 0
[[1,1,1,1,1,1],[1,1],[1]] => 0
[[1,1,1,1,1,1],[1,1,1]] => 0
[[7],[1],[1]] => 0
[[7],[2]] => 1
[[6,1],[1],[1]] => 1
[[6,1],[2]] => 2
[[6,1],[1,1]] => 1
[[5,2],[1],[1]] => 1
[[5,2],[2]] => 2
[[5,2],[1,1]] => 1
[[5,1,1],[1],[1]] => 0
[[5,1,1],[2]] => 1
[[5,1,1],[1,1]] => 0
[[4,3],[1],[1]] => 1
[[4,3],[2]] => 2
[[4,3],[1,1]] => 1
[[4,2,1],[1],[1]] => 2
[[4,2,1],[2]] => 3
[[4,2,1],[1,1]] => 2
[[4,1,1,1],[1],[1]] => 1
[[4,1,1,1],[2]] => 2
[[4,1,1,1],[1,1]] => 1
[[3,3,1],[1],[1]] => 0
[[3,3,1],[2]] => 1
[[3,3,1],[1,1]] => 0
[[3,2,2],[1],[1]] => 2
[[3,2,2],[2]] => 3
[[3,2,2],[1,1]] => 2
[[3,2,1,1],[1],[1]] => 1
[[3,2,1,1],[2]] => 2
[[3,2,1,1],[1,1]] => 1
[[3,1,1,1,1],[1],[1]] => 0
[[3,1,1,1,1],[2]] => 1
[[3,1,1,1,1],[1,1]] => 0
[[2,2,2,1],[1],[1]] => 3
[[2,2,2,1],[2]] => 4
[[2,2,2,1],[1,1]] => 3
[[2,2,1,1,1],[1],[1]] => 2
[[2,2,1,1,1],[2]] => 3
[[2,2,1,1,1],[1,1]] => 2
[[2,1,1,1,1,1],[1],[1]] => 1
[[2,1,1,1,1,1],[2]] => 2
[[2,1,1,1,1,1],[1,1]] => 1
[[1,1,1,1,1,1,1],[1],[1]] => 0
[[1,1,1,1,1,1,1],[1,1]] => 0
[[8],[1]] => 1
[[7,1],[1]] => 0
[[6,2],[1]] => 2
[[6,1,1],[1]] => 1
[[5,3],[1]] => 0
[[5,2,1],[1]] => 1
[[5,1,1,1],[1]] => 0
[[4,4],[1]] => 2
[[4,3,1],[1]] => 1
[[4,2,2],[1]] => 3
[[4,2,1,1],[1]] => 2
[[4,1,1,1,1],[1]] => 1
[[3,3,2],[1]] => 1
[[3,3,1,1],[1]] => 0
[[3,2,2,1],[1]] => 2
[[3,2,1,1,1],[1]] => 1
[[3,1,1,1,1,1],[1]] => 0
[[2,2,2,2],[1]] => 4
[[2,2,2,1,1],[1]] => 3
[[2,2,1,1,1,1],[1]] => 2
[[2,1,1,1,1,1,1],[1]] => 1
[[1,1,1,1,1,1,1,1],[1]] => 0
[[9]] => 0
[[8,1]] => 1
[[7,2]] => 1
[[7,1,1]] => 0
[[6,3]] => 1
[[6,2,1]] => 2
[[6,1,1,1]] => 1
[[5,4]] => 1
[[5,3,1]] => 0
[[5,2,2]] => 2
[[5,2,1,1]] => 1
[[5,1,1,1,1]] => 0
[[4,4,1]] => 2
[[4,3,2]] => 2
[[4,3,1,1]] => 1
[[4,2,2,1]] => 3
[[4,2,1,1,1]] => 2
[[4,1,1,1,1,1]] => 1
[[3,3,3]] => 0
[[3,3,2,1]] => 1
[[3,3,1,1,1]] => 0
[[3,2,2,2]] => 3
[[3,2,2,1,1]] => 2
[[3,2,1,1,1,1]] => 1
[[3,1,1,1,1,1,1]] => 0
[[2,2,2,2,1]] => 4
[[2,2,2,1,1,1]] => 3
[[2,2,1,1,1,1,1]] => 2
[[2,1,1,1,1,1,1,1]] => 1
[[1,1,1,1,1,1,1,1,1]] => 0
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => 0
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => 1
[[2],[2],[1],[1],[1],[1],[1],[1]] => 2
[[2],[2],[2],[1],[1],[1],[1]] => 3
[[2],[2],[2],[2],[1],[1]] => 4
[[2],[2],[2],[2],[2]] => 5
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => 0
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => 0
[[1,1],[1,1],[1,1],[1,1],[1,1]] => 0
[[3],[1],[1],[1],[1],[1],[1],[1]] => 0
[[3],[2],[1],[1],[1],[1],[1]] => 1
[[3],[2],[2],[1],[1],[1]] => 2
[[3],[2],[2],[2],[1]] => 3
[[3],[3],[1],[1],[1],[1]] => 0
[[3],[3],[2],[1],[1]] => 1
[[3],[3],[2],[2]] => 2
[[3],[3],[3],[1]] => 0
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => 1
[[2,1],[2],[1],[1],[1],[1],[1]] => 2
[[2,1],[2],[2],[1],[1],[1]] => 3
[[2,1],[2],[2],[2],[1]] => 4
[[2,1],[1,1],[1],[1],[1],[1],[1]] => 1
[[2,1],[1,1],[1,1],[1],[1],[1]] => 1
[[2,1],[1,1],[1,1],[1,1],[1]] => 1
[[2,1],[2,1],[1],[1],[1],[1]] => 2
[[2,1],[2,1],[2],[1],[1]] => 3
[[2,1],[2,1],[2],[2]] => 4
[[2,1],[2,1],[1,1],[1],[1]] => 2
[[2,1],[2,1],[1,1],[1,1]] => 2
[[2,1],[2,1],[2,1],[1]] => 3
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => 0
[[1,1,1],[1,1],[1,1],[1,1],[1]] => 0
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => 0
[[1,1,1],[1,1,1],[1,1],[1],[1]] => 0
[[1,1,1],[1,1,1],[1,1],[1,1]] => 0
[[1,1,1],[1,1,1],[1,1,1],[1]] => 0
[[4],[1],[1],[1],[1],[1],[1]] => 1
[[4],[2],[1],[1],[1],[1]] => 2
[[4],[2],[2],[1],[1]] => 3
[[4],[2],[2],[2]] => 4
[[4],[3],[1],[1],[1]] => 1
[[4],[3],[2],[1]] => 2
[[4],[3],[3]] => 1
[[4],[4],[1],[1]] => 2
[[4],[4],[2]] => 3
[[3,1],[1],[1],[1],[1],[1],[1]] => 0
[[3,1],[2],[1],[1],[1],[1]] => 1
[[3,1],[2],[2],[1],[1]] => 2
[[3,1],[2],[2],[2]] => 3
[[3,1],[1,1],[1],[1],[1],[1]] => 0
[[3,1],[1,1],[1,1],[1],[1]] => 0
[[3,1],[1,1],[1,1],[1,1]] => 0
[[3,1],[3],[1],[1],[1]] => 0
[[3,1],[3],[2],[1]] => 1
[[3,1],[3],[3]] => 0
[[3,1],[2,1],[1],[1],[1]] => 1
[[3,1],[2,1],[2],[1]] => 2
[[3,1],[2,1],[1,1],[1]] => 1
[[3,1],[2,1],[2,1]] => 2
[[3,1],[3,1],[1],[1]] => 0
[[3,1],[3,1],[2]] => 1
[[3,1],[3,1],[1,1]] => 0
[[2,2],[1],[1],[1],[1],[1],[1]] => 2
[[2,2],[2],[1],[1],[1],[1]] => 3
[[2,2],[2],[2],[1],[1]] => 4
[[2,2],[2],[2],[2]] => 5
[[2,2],[1,1],[1],[1],[1],[1]] => 2
[[2,2],[1,1],[1,1],[1],[1]] => 2
[[2,2],[1,1],[1,1],[1,1]] => 2
[[2,2],[2,1],[1],[1],[1]] => 3
[[2,2],[2,1],[2],[1]] => 4
[[2,2],[2,1],[1,1],[1]] => 3
[[2,2],[2,1],[2,1]] => 4
[[2,2],[2,2],[1],[1]] => 4
[[2,2],[2,2],[2]] => 5
[[2,2],[2,2],[1,1]] => 4
[[2,1,1],[1],[1],[1],[1],[1],[1]] => 1
[[2,1,1],[2],[1],[1],[1],[1]] => 2
[[2,1,1],[2],[2],[1],[1]] => 3
[[2,1,1],[2],[2],[2]] => 4
[[2,1,1],[1,1],[1],[1],[1],[1]] => 1
[[2,1,1],[1,1],[1,1],[1],[1]] => 1
[[2,1,1],[1,1],[1,1],[1,1]] => 1
[[2,1,1],[2,1],[1],[1],[1]] => 2
[[2,1,1],[2,1],[2],[1]] => 3
[[2,1,1],[2,1],[1,1],[1]] => 2
[[2,1,1],[2,1],[2,1]] => 3
[[2,1,1],[1,1,1],[1],[1],[1]] => 1
[[2,1,1],[1,1,1],[1,1],[1]] => 1
[[2,1,1],[1,1,1],[1,1,1]] => 1
[[2,1,1],[2,1,1],[1],[1]] => 2
[[2,1,1],[2,1,1],[2]] => 3
[[2,1,1],[2,1,1],[1,1]] => 2
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1,1],[1],[1]] => 0
[[1,1,1,1],[1,1],[1,1],[1,1]] => 0
[[1,1,1,1],[1,1,1],[1],[1],[1]] => 0
[[1,1,1,1],[1,1,1],[1,1],[1]] => 0
[[1,1,1,1],[1,1,1],[1,1,1]] => 0
[[1,1,1,1],[1,1,1,1],[1],[1]] => 0
[[1,1,1,1],[1,1,1,1],[1,1]] => 0
[[5],[1],[1],[1],[1],[1]] => 0
[[5],[2],[1],[1],[1]] => 1
[[5],[2],[2],[1]] => 2
[[5],[3],[1],[1]] => 0
[[5],[3],[2]] => 1
[[5],[4],[1]] => 1
[[5],[5]] => 0
[[4,1],[1],[1],[1],[1],[1]] => 1
[[4,1],[2],[1],[1],[1]] => 2
[[4,1],[2],[2],[1]] => 3
[[4,1],[1,1],[1],[1],[1]] => 1
[[4,1],[1,1],[1,1],[1]] => 1
[[4,1],[3],[1],[1]] => 1
[[4,1],[3],[2]] => 2
[[4,1],[2,1],[1],[1]] => 2
[[4,1],[2,1],[2]] => 3
[[4,1],[2,1],[1,1]] => 2
[[4,1],[4],[1]] => 2
[[4,1],[3,1],[1]] => 1
[[4,1],[4,1]] => 2
[[3,2],[1],[1],[1],[1],[1]] => 1
[[3,2],[2],[1],[1],[1]] => 2
[[3,2],[2],[2],[1]] => 3
[[3,2],[1,1],[1],[1],[1]] => 1
[[3,2],[1,1],[1,1],[1]] => 1
[[3,2],[3],[1],[1]] => 1
[[3,2],[3],[2]] => 2
[[3,2],[2,1],[1],[1]] => 2
[[3,2],[2,1],[2]] => 3
[[3,2],[2,1],[1,1]] => 2
[[3,2],[3,1],[1]] => 1
[[3,2],[2,2],[1]] => 3
[[3,2],[3,2]] => 2
[[3,1,1],[1],[1],[1],[1],[1]] => 0
[[3,1,1],[2],[1],[1],[1]] => 1
[[3,1,1],[2],[2],[1]] => 2
[[3,1,1],[1,1],[1],[1],[1]] => 0
[[3,1,1],[1,1],[1,1],[1]] => 0
[[3,1,1],[3],[1],[1]] => 0
[[3,1,1],[3],[2]] => 1
[[3,1,1],[2,1],[1],[1]] => 1
[[3,1,1],[2,1],[2]] => 2
[[3,1,1],[2,1],[1,1]] => 1
[[3,1,1],[1,1,1],[1],[1]] => 0
[[3,1,1],[1,1,1],[1,1]] => 0
[[3,1,1],[3,1],[1]] => 0
[[3,1,1],[2,1,1],[1]] => 1
[[3,1,1],[3,1,1]] => 0
[[2,2,1],[1],[1],[1],[1],[1]] => 2
[[2,2,1],[2],[1],[1],[1]] => 3
[[2,2,1],[2],[2],[1]] => 4
[[2,2,1],[1,1],[1],[1],[1]] => 2
[[2,2,1],[1,1],[1,1],[1]] => 2
[[2,2,1],[2,1],[1],[1]] => 3
[[2,2,1],[2,1],[2]] => 4
[[2,2,1],[2,1],[1,1]] => 3
[[2,2,1],[1,1,1],[1],[1]] => 2
[[2,2,1],[1,1,1],[1,1]] => 2
[[2,2,1],[2,2],[1]] => 4
[[2,2,1],[2,1,1],[1]] => 3
[[2,2,1],[2,2,1]] => 4
[[2,1,1,1],[1],[1],[1],[1],[1]] => 1
[[2,1,1,1],[2],[1],[1],[1]] => 2
[[2,1,1,1],[2],[2],[1]] => 3
[[2,1,1,1],[1,1],[1],[1],[1]] => 1
[[2,1,1,1],[1,1],[1,1],[1]] => 1
[[2,1,1,1],[2,1],[1],[1]] => 2
[[2,1,1,1],[2,1],[2]] => 3
[[2,1,1,1],[2,1],[1,1]] => 2
[[2,1,1,1],[1,1,1],[1],[1]] => 1
[[2,1,1,1],[1,1,1],[1,1]] => 1
[[2,1,1,1],[2,1,1],[1]] => 2
[[2,1,1,1],[1,1,1,1],[1]] => 1
[[2,1,1,1],[2,1,1,1]] => 2
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => 0
[[1,1,1,1,1],[1,1],[1],[1],[1]] => 0
[[1,1,1,1,1],[1,1],[1,1],[1]] => 0
[[1,1,1,1,1],[1,1,1],[1],[1]] => 0
[[1,1,1,1,1],[1,1,1],[1,1]] => 0
[[1,1,1,1,1],[1,1,1,1],[1]] => 0
[[1,1,1,1,1],[1,1,1,1,1]] => 0
[[6],[1],[1],[1],[1]] => 1
[[6],[2],[1],[1]] => 2
[[6],[2],[2]] => 3
[[6],[3],[1]] => 1
[[6],[4]] => 2
[[5,1],[1],[1],[1],[1]] => 0
[[5,1],[2],[1],[1]] => 1
[[5,1],[2],[2]] => 2
[[5,1],[1,1],[1],[1]] => 0
[[5,1],[1,1],[1,1]] => 0
[[5,1],[3],[1]] => 0
[[5,1],[2,1],[1]] => 1
[[5,1],[4]] => 1
[[5,1],[3,1]] => 0
[[4,2],[1],[1],[1],[1]] => 2
[[4,2],[2],[1],[1]] => 3
[[4,2],[2],[2]] => 4
[[4,2],[1,1],[1],[1]] => 2
[[4,2],[1,1],[1,1]] => 2
[[4,2],[3],[1]] => 2
[[4,2],[2,1],[1]] => 3
[[4,2],[4]] => 3
[[4,2],[3,1]] => 2
[[4,2],[2,2]] => 4
[[4,1,1],[1],[1],[1],[1]] => 1
[[4,1,1],[2],[1],[1]] => 2
[[4,1,1],[2],[2]] => 3
[[4,1,1],[1,1],[1],[1]] => 1
[[4,1,1],[1,1],[1,1]] => 1
[[4,1,1],[3],[1]] => 1
[[4,1,1],[2,1],[1]] => 2
[[4,1,1],[1,1,1],[1]] => 1
[[4,1,1],[4]] => 2
[[4,1,1],[3,1]] => 1
[[4,1,1],[2,1,1]] => 2
[[3,3],[1],[1],[1],[1]] => 0
[[3,3],[2],[1],[1]] => 1
[[3,3],[2],[2]] => 2
[[3,3],[1,1],[1],[1]] => 0
[[3,3],[1,1],[1,1]] => 0
[[3,3],[3],[1]] => 0
[[3,3],[2,1],[1]] => 1
[[3,3],[3,1]] => 0
[[3,3],[2,2]] => 2
[[3,2,1],[1],[1],[1],[1]] => 1
[[3,2,1],[2],[1],[1]] => 2
[[3,2,1],[2],[2]] => 3
[[3,2,1],[1,1],[1],[1]] => 1
[[3,2,1],[1,1],[1,1]] => 1
[[3,2,1],[3],[1]] => 1
[[3,2,1],[2,1],[1]] => 2
[[3,2,1],[1,1,1],[1]] => 1
[[3,2,1],[3,1]] => 1
[[3,2,1],[2,2]] => 3
[[3,2,1],[2,1,1]] => 2
[[3,1,1,1],[1],[1],[1],[1]] => 0
[[3,1,1,1],[2],[1],[1]] => 1
[[3,1,1,1],[2],[2]] => 2
[[3,1,1,1],[1,1],[1],[1]] => 0
[[3,1,1,1],[1,1],[1,1]] => 0
[[3,1,1,1],[3],[1]] => 0
[[3,1,1,1],[2,1],[1]] => 1
[[3,1,1,1],[1,1,1],[1]] => 0
[[3,1,1,1],[3,1]] => 0
[[3,1,1,1],[2,1,1]] => 1
[[3,1,1,1],[1,1,1,1]] => 0
[[2,2,2],[1],[1],[1],[1]] => 3
[[2,2,2],[2],[1],[1]] => 4
[[2,2,2],[2],[2]] => 5
[[2,2,2],[1,1],[1],[1]] => 3
[[2,2,2],[1,1],[1,1]] => 3
[[2,2,2],[2,1],[1]] => 4
[[2,2,2],[1,1,1],[1]] => 3
[[2,2,2],[2,2]] => 5
[[2,2,2],[2,1,1]] => 4
[[2,2,1,1],[1],[1],[1],[1]] => 2
[[2,2,1,1],[2],[1],[1]] => 3
[[2,2,1,1],[2],[2]] => 4
[[2,2,1,1],[1,1],[1],[1]] => 2
[[2,2,1,1],[1,1],[1,1]] => 2
[[2,2,1,1],[2,1],[1]] => 3
[[2,2,1,1],[1,1,1],[1]] => 2
[[2,2,1,1],[2,2]] => 4
[[2,2,1,1],[2,1,1]] => 3
[[2,2,1,1],[1,1,1,1]] => 2
[[2,1,1,1,1],[1],[1],[1],[1]] => 1
[[2,1,1,1,1],[2],[1],[1]] => 2
[[2,1,1,1,1],[2],[2]] => 3
[[2,1,1,1,1],[1,1],[1],[1]] => 1
[[2,1,1,1,1],[1,1],[1,1]] => 1
[[2,1,1,1,1],[2,1],[1]] => 2
[[2,1,1,1,1],[1,1,1],[1]] => 1
[[2,1,1,1,1],[2,1,1]] => 2
[[2,1,1,1,1],[1,1,1,1]] => 1
[[1,1,1,1,1,1],[1],[1],[1],[1]] => 0
[[1,1,1,1,1,1],[1,1],[1],[1]] => 0
[[1,1,1,1,1,1],[1,1],[1,1]] => 0
[[1,1,1,1,1,1],[1,1,1],[1]] => 0
[[1,1,1,1,1,1],[1,1,1,1]] => 0
[[7],[1],[1],[1]] => 0
[[7],[2],[1]] => 1
[[7],[3]] => 0
[[6,1],[1],[1],[1]] => 1
[[6,1],[2],[1]] => 2
[[6,1],[1,1],[1]] => 1
[[6,1],[3]] => 1
[[6,1],[2,1]] => 2
[[5,2],[1],[1],[1]] => 1
[[5,2],[2],[1]] => 2
[[5,2],[1,1],[1]] => 1
[[5,2],[3]] => 1
[[5,2],[2,1]] => 2
[[5,1,1],[1],[1],[1]] => 0
[[5,1,1],[2],[1]] => 1
[[5,1,1],[1,1],[1]] => 0
[[5,1,1],[3]] => 0
[[5,1,1],[2,1]] => 1
[[5,1,1],[1,1,1]] => 0
[[4,3],[1],[1],[1]] => 1
[[4,3],[2],[1]] => 2
[[4,3],[1,1],[1]] => 1
[[4,3],[3]] => 1
[[4,3],[2,1]] => 2
[[4,2,1],[1],[1],[1]] => 2
[[4,2,1],[2],[1]] => 3
[[4,2,1],[1,1],[1]] => 2
[[4,2,1],[3]] => 2
[[4,2,1],[2,1]] => 3
[[4,2,1],[1,1,1]] => 2
[[4,1,1,1],[1],[1],[1]] => 1
[[4,1,1,1],[2],[1]] => 2
[[4,1,1,1],[1,1],[1]] => 1
[[4,1,1,1],[3]] => 1
[[4,1,1,1],[2,1]] => 2
[[4,1,1,1],[1,1,1]] => 1
[[3,3,1],[1],[1],[1]] => 0
[[3,3,1],[2],[1]] => 1
[[3,3,1],[1,1],[1]] => 0
[[3,3,1],[3]] => 0
[[3,3,1],[2,1]] => 1
[[3,3,1],[1,1,1]] => 0
[[3,2,2],[1],[1],[1]] => 2
[[3,2,2],[2],[1]] => 3
[[3,2,2],[1,1],[1]] => 2
[[3,2,2],[3]] => 2
[[3,2,2],[2,1]] => 3
[[3,2,2],[1,1,1]] => 2
[[3,2,1,1],[1],[1],[1]] => 1
[[3,2,1,1],[2],[1]] => 2
[[3,2,1,1],[1,1],[1]] => 1
[[3,2,1,1],[3]] => 1
[[3,2,1,1],[2,1]] => 2
[[3,2,1,1],[1,1,1]] => 1
[[3,1,1,1,1],[1],[1],[1]] => 0
[[3,1,1,1,1],[2],[1]] => 1
[[3,1,1,1,1],[1,1],[1]] => 0
[[3,1,1,1,1],[3]] => 0
[[3,1,1,1,1],[2,1]] => 1
[[3,1,1,1,1],[1,1,1]] => 0
[[2,2,2,1],[1],[1],[1]] => 3
[[2,2,2,1],[2],[1]] => 4
[[2,2,2,1],[1,1],[1]] => 3
[[2,2,2,1],[2,1]] => 4
[[2,2,2,1],[1,1,1]] => 3
[[2,2,1,1,1],[1],[1],[1]] => 2
[[2,2,1,1,1],[2],[1]] => 3
[[2,2,1,1,1],[1,1],[1]] => 2
[[2,2,1,1,1],[2,1]] => 3
[[2,2,1,1,1],[1,1,1]] => 2
[[2,1,1,1,1,1],[1],[1],[1]] => 1
[[2,1,1,1,1,1],[2],[1]] => 2
[[2,1,1,1,1,1],[1,1],[1]] => 1
[[2,1,1,1,1,1],[2,1]] => 2
[[2,1,1,1,1,1],[1,1,1]] => 1
[[1,1,1,1,1,1,1],[1],[1],[1]] => 0
[[1,1,1,1,1,1,1],[1,1],[1]] => 0
[[1,1,1,1,1,1,1],[1,1,1]] => 0
[[8],[1],[1]] => 1
[[8],[2]] => 2
[[7,1],[1],[1]] => 0
[[7,1],[2]] => 1
[[7,1],[1,1]] => 0
[[6,2],[1],[1]] => 2
[[6,2],[2]] => 3
[[6,2],[1,1]] => 2
[[6,1,1],[1],[1]] => 1
[[6,1,1],[2]] => 2
[[6,1,1],[1,1]] => 1
[[5,3],[1],[1]] => 0
[[5,3],[2]] => 1
[[5,3],[1,1]] => 0
[[5,2,1],[1],[1]] => 1
[[5,2,1],[2]] => 2
[[5,2,1],[1,1]] => 1
[[5,1,1,1],[1],[1]] => 0
[[5,1,1,1],[2]] => 1
[[5,1,1,1],[1,1]] => 0
[[4,4],[1],[1]] => 2
[[4,4],[2]] => 3
[[4,4],[1,1]] => 2
[[4,3,1],[1],[1]] => 1
[[4,3,1],[2]] => 2
[[4,3,1],[1,1]] => 1
[[4,2,2],[1],[1]] => 3
[[4,2,2],[2]] => 4
[[4,2,2],[1,1]] => 3
[[4,2,1,1],[1],[1]] => 2
[[4,2,1,1],[2]] => 3
[[4,2,1,1],[1,1]] => 2
[[4,1,1,1,1],[1],[1]] => 1
[[4,1,1,1,1],[2]] => 2
[[4,1,1,1,1],[1,1]] => 1
[[3,3,2],[1],[1]] => 1
[[3,3,2],[2]] => 2
[[3,3,2],[1,1]] => 1
[[3,3,1,1],[1],[1]] => 0
[[3,3,1,1],[2]] => 1
[[3,3,1,1],[1,1]] => 0
[[3,2,2,1],[1],[1]] => 2
[[3,2,2,1],[2]] => 3
[[3,2,2,1],[1,1]] => 2
[[3,2,1,1,1],[1],[1]] => 1
[[3,2,1,1,1],[2]] => 2
[[3,2,1,1,1],[1,1]] => 1
[[3,1,1,1,1,1],[1],[1]] => 0
[[3,1,1,1,1,1],[2]] => 1
[[3,1,1,1,1,1],[1,1]] => 0
[[2,2,2,2],[1],[1]] => 4
[[2,2,2,2],[2]] => 5
[[2,2,2,2],[1,1]] => 4
[[2,2,2,1,1],[1],[1]] => 3
[[2,2,2,1,1],[2]] => 4
[[2,2,2,1,1],[1,1]] => 3
[[2,2,1,1,1,1],[1],[1]] => 2
[[2,2,1,1,1,1],[2]] => 3
[[2,2,1,1,1,1],[1,1]] => 2
[[2,1,1,1,1,1,1],[1],[1]] => 1
[[2,1,1,1,1,1,1],[2]] => 2
[[2,1,1,1,1,1,1],[1,1]] => 1
[[1,1,1,1,1,1,1,1],[1],[1]] => 0
[[1,1,1,1,1,1,1,1],[1,1]] => 0
[[9],[1]] => 0
[[8,1],[1]] => 1
[[7,2],[1]] => 1
[[7,1,1],[1]] => 0
[[6,3],[1]] => 1
[[6,2,1],[1]] => 2
[[6,1,1,1],[1]] => 1
[[5,4],[1]] => 1
[[5,3,1],[1]] => 0
[[5,2,2],[1]] => 2
[[5,2,1,1],[1]] => 1
[[5,1,1,1,1],[1]] => 0
[[4,4,1],[1]] => 2
[[4,3,2],[1]] => 2
[[4,3,1,1],[1]] => 1
[[4,2,2,1],[1]] => 3
[[4,2,1,1,1],[1]] => 2
[[4,1,1,1,1,1],[1]] => 1
[[3,3,3],[1]] => 0
[[3,3,2,1],[1]] => 1
[[3,3,1,1,1],[1]] => 0
[[3,2,2,2],[1]] => 3
[[3,2,2,1,1],[1]] => 2
[[3,2,1,1,1,1],[1]] => 1
[[3,1,1,1,1,1,1],[1]] => 0
[[2,2,2,2,1],[1]] => 4
[[2,2,2,1,1,1],[1]] => 3
[[2,2,1,1,1,1,1],[1]] => 2
[[2,1,1,1,1,1,1,1],[1]] => 1
[[1,1,1,1,1,1,1,1,1],[1]] => 0
[[10]] => 1
[[9,1]] => 0
[[8,2]] => 2
[[8,1,1]] => 1
[[7,3]] => 0
[[7,2,1]] => 1
[[7,1,1,1]] => 0
[[6,4]] => 2
[[6,3,1]] => 1
[[6,2,2]] => 3
[[6,2,1,1]] => 2
[[6,1,1,1,1]] => 1
[[5,5]] => 0
[[5,4,1]] => 1
[[5,3,2]] => 1
[[5,3,1,1]] => 0
[[5,2,2,1]] => 2
[[5,2,1,1,1]] => 1
[[5,1,1,1,1,1]] => 0
[[4,4,2]] => 3
[[4,4,1,1]] => 2
[[4,3,3]] => 1
[[4,3,2,1]] => 2
[[4,3,1,1,1]] => 1
[[4,2,2,2]] => 4
[[4,2,2,1,1]] => 3
[[4,2,1,1,1,1]] => 2
[[4,1,1,1,1,1,1]] => 1
[[3,3,3,1]] => 0
[[3,3,2,2]] => 2
[[3,3,2,1,1]] => 1
[[3,3,1,1,1,1]] => 0
[[3,2,2,2,1]] => 3
[[3,2,2,1,1,1]] => 2
[[3,2,1,1,1,1,1]] => 1
[[3,1,1,1,1,1,1,1]] => 0
[[2,2,2,2,2]] => 5
[[2,2,2,2,1,1]] => 4
[[2,2,2,1,1,1,1]] => 3
[[2,2,1,1,1,1,1,1]] => 2
[[2,1,1,1,1,1,1,1,1]] => 1
[[1,1,1,1,1,1,1,1,1,1]] => 0
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
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 4,2 7,4,2 11,9,4 20,15,10,3 30,30,19,7 50,50,39,16,5 75,92,68,35,12 121,145,130,67,30,7
$F_{1} = 1$
$F_{2} = 2 + q$
$F_{3} = 4 + 2\ q$
$F_{4} = 7 + 4\ q + 2\ q^{2}$
$F_{5} = 11 + 9\ q + 4\ q^{2}$
$F_{6} = 20 + 15\ q + 10\ q^{2} + 3\ q^{3}$
$F_{7} = 30 + 30\ q + 19\ q^{2} + 7\ q^{3}$
$F_{8} = 50 + 50\ q + 39\ q^{2} + 16\ q^{3} + 5\ q^{4}$
$F_{9} = 75 + 92\ q + 68\ q^{2} + 35\ q^{3} + 12\ q^{4}$
$F_{10} = 121 + 145\ q + 130\ q^{2} + 67\ q^{3} + 30\ q^{4} + 7\ q^{5}$
Description
Number of even parts in the plane partition.
Code
def statistic(P):
return sum(1 for row in P for i in row if is_even(i))
Created
Jul 26, 2019 at 19:50 by Erika Pirnes
Updated
Jul 27, 2019 at 16:33 by Christian Stump
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!