Identifier
Values
[1] => [1] => [[1],[]] => [[1],[]] => 0
[2] => [1,1] => [[1,1],[]] => [[1,1],[]] => 0
[1,1] => [2] => [[2],[]] => [[2],[]] => 0
[3] => [1,1,1] => [[1,1,1],[]] => [[1,1,1],[]] => 0
[2,1] => [2,1] => [[2,1],[]] => [[2,2],[1]] => 1
[1,1,1] => [3] => [[3],[]] => [[3],[]] => 0
[4] => [1,1,1,1] => [[1,1,1,1],[]] => [[1,1,1,1],[]] => 0
[3,1] => [2,1,1] => [[2,1,1],[]] => [[2,2,2],[1,1]] => 1
[2,2] => [2,2] => [[2,2],[]] => [[2,2],[]] => 0
[2,1,1] => [3,1] => [[3,1],[]] => [[3,3],[2]] => 2
[1,1,1,1] => [4] => [[4],[]] => [[4],[]] => 0
[5] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => 0
[4,1] => [2,1,1,1] => [[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => 1
[3,2] => [2,2,1] => [[2,2,1],[]] => [[2,2,2],[1]] => 1
[3,1,1] => [3,1,1] => [[3,1,1],[]] => [[3,3,3],[2,2]] => 2
[2,2,1] => [3,2] => [[3,2],[]] => [[3,3],[1]] => 1
[2,1,1,1] => [4,1] => [[4,1],[]] => [[4,4],[3]] => 3
[1,1,1,1,1] => [5] => [[5],[]] => [[5],[]] => 0
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Description
The number of missing boxes in the first row.
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to skew partition
Description
The partition regarded as a skew partition.
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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.
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conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.