Identifier
-
Mp00207:
Standard tableaux
—horizontal strip sizes⟶
Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
St001488: Skew partitions ⟶ ℤ
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.
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 $i$.
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.
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.
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