Identifier
Values
[[1],[]] => [[1],[]] => 0
[[2],[]] => [[2],[]] => 0
[[1,1],[]] => [[1,1],[]] => 0
[[2,1],[1]] => [[2,1],[1]] => 1
[[3],[]] => [[3],[]] => 0
[[2,1],[]] => [[2,2],[1]] => 1
[[3,1],[1]] => [[3,2],[2]] => 2
[[2,2],[1]] => [[2,1],[]] => 0
[[3,2],[2]] => [[3,1],[1]] => 1
[[1,1,1],[]] => [[1,1,1],[]] => 0
[[2,2,1],[1,1]] => [[2,1,1],[1]] => 1
[[2,1,1],[1]] => [[2,2,1],[1,1]] => 2
[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => 3
[[4],[]] => [[4],[]] => 0
[[3,1],[]] => [[3,3],[2]] => 2
[[4,1],[1]] => [[4,3],[3]] => 3
[[2,2],[]] => [[2,2],[]] => 0
[[3,2],[1]] => [[3,2],[1]] => 1
[[4,2],[2]] => [[4,2],[2]] => 2
[[2,1,1],[]] => [[2,2,2],[1,1]] => 2
[[3,2,1],[1,1]] => [[3,2,2],[2,1]] => 3
[[3,1,1],[1]] => [[3,3,2],[2,2]] => 4
[[4,2,1],[2,1]] => [[4,3,2],[3,2]] => 5
[[3,3],[2]] => [[3,1],[]] => 0
[[4,3],[3]] => [[4,1],[1]] => 1
[[2,2,1],[1]] => [[2,2,1],[1]] => 1
[[3,3,1],[2,1]] => [[3,2,1],[2]] => 2
[[3,2,1],[2]] => [[3,3,1],[2,1]] => 3
[[4,3,1],[3,1]] => [[4,3,1],[3,1]] => 4
[[2,2,2],[1,1]] => [[2,1,1],[]] => 0
[[3,3,2],[2,2]] => [[3,1,1],[1]] => 1
[[3,2,2],[2,1]] => [[3,2,1],[1,1]] => 2
[[4,3,2],[3,2]] => [[4,2,1],[2,1]] => 3
[[1,1,1,1],[]] => [[1,1,1,1],[]] => 0
[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] => 1
[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] => 2
[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] => 3
[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] => 3
[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] => 4
[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] => 5
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => 6
[[5],[]] => [[5],[]] => 0
[[4,1],[]] => [[4,4],[3]] => 3
[[5,1],[1]] => [[5,4],[4]] => 4
[[3,2],[]] => [[3,3],[1]] => 1
[[4,2],[1]] => [[4,3],[2]] => 2
[[5,2],[2]] => [[5,3],[3]] => 3
[[3,1,1],[]] => [[3,3,3],[2,2]] => 4
[[4,2,1],[1,1]] => [[4,3,3],[3,2]] => 5
[[4,1,1],[1]] => [[4,4,3],[3,3]] => 6
[[5,2,1],[2,1]] => [[5,4,3],[4,3]] => 7
[[3,3],[1]] => [[3,2],[]] => 0
[[4,3],[2]] => [[4,2],[1]] => 1
[[5,3],[3]] => [[5,2],[2]] => 2
[[2,2,1],[]] => [[2,2,2],[1]] => 1
[[3,3,1],[1,1]] => [[3,2,2],[2]] => 2
[[3,2,1],[1]] => [[3,3,2],[2,1]] => 3
[[4,3,1],[2,1]] => [[4,3,2],[3,1]] => 4
[[4,2,1],[2]] => [[4,4,2],[3,2]] => 5
[[5,3,1],[3,1]] => [[5,4,2],[4,2]] => 6
[[3,2,2],[1,1]] => [[3,2,2],[1,1]] => 2
[[4,3,2],[2,2]] => [[4,2,2],[2,1]] => 3
[[4,2,2],[2,1]] => [[4,3,2],[2,2]] => 4
[[5,3,2],[3,2]] => [[5,3,2],[3,2]] => 5
[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => 3
[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] => 4
[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] => 5
[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] => 6
[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] => 6
[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] => 7
[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] => 8
[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] => 9
[[4,4],[3]] => [[4,1],[]] => 0
[[5,4],[4]] => [[5,1],[1]] => 1
[[3,3,1],[2]] => [[3,3,1],[2]] => 2
[[4,4,1],[3,1]] => [[4,3,1],[3]] => 3
[[4,3,1],[3]] => [[4,4,1],[3,1]] => 4
[[5,4,1],[4,1]] => [[5,4,1],[4,1]] => 5
[[2,2,2],[1]] => [[2,2,1],[]] => 0
[[3,3,2],[2,1]] => [[3,2,1],[1]] => 1
[[4,4,2],[3,2]] => [[4,2,1],[2]] => 2
[[3,2,2],[2]] => [[3,3,1],[1,1]] => 2
[[4,3,2],[3,1]] => [[4,3,1],[2,1]] => 3
[[5,4,2],[4,2]] => [[5,3,1],[3,1]] => 4
[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] => 2
[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] => 3
[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] => 4
[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] => 5
[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] => 5
[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] => 6
[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] => 7
[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] => 8
[[3,3,3],[2,2]] => [[3,1,1],[]] => 0
[[4,4,3],[3,3]] => [[4,1,1],[1]] => 1
[[4,3,3],[3,2]] => [[4,2,1],[1,1]] => 2
[[5,4,3],[4,3]] => [[5,2,1],[2,1]] => 3
[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] => 1
[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] => 2
[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] => 3
[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] => 4
[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] => 4
>>> Load all 128 entries. <<<
[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] => 5
[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] => 6
[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] => 7
[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] => 0
[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] => 1
[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] => 2
[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] => 3
[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] => 3
[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] => 4
[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] => 5
[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] => 6
[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => 0
[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] => 1
[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] => 2
[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] => 3
[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] => 3
[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] => 4
[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] => 5
[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] => 6
[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] => 4
[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] => 5
[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] => 6
[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => 7
[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] => 7
[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] => 8
[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] => 9
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => 10
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Description
The number of missing boxes of a skew partition.
Map
rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.