Identifier
Values
[[1]] => [1] => [[1],[]] => 1
[[1,2]] => [2] => [[2],[]] => 2
[[1],[2]] => [1,1] => [[1,1],[]] => 2
[[1,2,3]] => [3] => [[3],[]] => 2
[[1,3],[2]] => [1,2] => [[2,1],[]] => 3
[[1,2],[3]] => [2,1] => [[2,2],[1]] => 3
[[1],[2],[3]] => [1,1,1] => [[1,1,1],[]] => 2
[[1,2,3,4]] => [4] => [[4],[]] => 2
[[1,3,4],[2]] => [1,3] => [[3,1],[]] => 3
[[1,2,4],[3]] => [2,2] => [[3,2],[1]] => 4
[[1,2,3],[4]] => [3,1] => [[3,3],[2]] => 3
[[1,3],[2,4]] => [1,2,1] => [[2,2,1],[1]] => 4
[[1,2],[3,4]] => [2,2] => [[3,2],[1]] => 4
[[1,4],[2],[3]] => [1,1,2] => [[2,1,1],[]] => 3
[[1,3],[2],[4]] => [1,2,1] => [[2,2,1],[1]] => 4
[[1,2],[3],[4]] => [2,1,1] => [[2,2,2],[1,1]] => 3
[[1],[2],[3],[4]] => [1,1,1,1] => [[1,1,1,1],[]] => 2
[[1,2,3,4,5]] => [5] => [[5],[]] => 2
[[1,3,4,5],[2]] => [1,4] => [[4,1],[]] => 3
[[1,2,4,5],[3]] => [2,3] => [[4,2],[1]] => 4
[[1,2,3,5],[4]] => [3,2] => [[4,3],[2]] => 4
[[1,2,3,4],[5]] => [4,1] => [[4,4],[3]] => 3
[[1,3,5],[2,4]] => [1,2,2] => [[3,2,1],[1]] => 5
[[1,2,5],[3,4]] => [2,3] => [[4,2],[1]] => 4
[[1,3,4],[2,5]] => [1,3,1] => [[3,3,1],[2]] => 4
[[1,2,4],[3,5]] => [2,2,1] => [[3,3,2],[2,1]] => 5
[[1,2,3],[4,5]] => [3,2] => [[4,3],[2]] => 4
[[1,4,5],[2],[3]] => [1,1,3] => [[3,1,1],[]] => 3
[[1,3,5],[2],[4]] => [1,2,2] => [[3,2,1],[1]] => 5
[[1,2,5],[3],[4]] => [2,1,2] => [[3,2,2],[1,1]] => 4
[[1,3,4],[2],[5]] => [1,3,1] => [[3,3,1],[2]] => 4
[[1,2,4],[3],[5]] => [2,2,1] => [[3,3,2],[2,1]] => 5
[[1,2,3],[4],[5]] => [3,1,1] => [[3,3,3],[2,2]] => 3
[[1,4],[2,5],[3]] => [1,1,2,1] => [[2,2,1,1],[1]] => 4
[[1,3],[2,5],[4]] => [1,2,2] => [[3,2,1],[1]] => 5
[[1,2],[3,5],[4]] => [2,1,2] => [[3,2,2],[1,1]] => 4
[[1,3],[2,4],[5]] => [1,2,1,1] => [[2,2,2,1],[1,1]] => 4
[[1,2],[3,4],[5]] => [2,2,1] => [[3,3,2],[2,1]] => 5
[[1,5],[2],[3],[4]] => [1,1,1,2] => [[2,1,1,1],[]] => 3
[[1,4],[2],[3],[5]] => [1,1,2,1] => [[2,2,1,1],[1]] => 4
[[1,3],[2],[4],[5]] => [1,2,1,1] => [[2,2,2,1],[1,1]] => 4
[[1,2],[3],[4],[5]] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 3
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
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Description
The number of corners of a skew partition.
This is also known as the number of removable cells of the skew partition.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.