Identifier
Values
[1] => [[1]] => [1] => 0
[2] => [[1,2]] => [2] => 0
[1,1] => [[1],[2]] => [1,1] => 0
[3] => [[1,2,3]] => [3] => 0
[2,1] => [[1,3],[2]] => [1,2] => 1
[1,1,1] => [[1],[2],[3]] => [1,1,1] => 0
[4] => [[1,2,3,4]] => [4] => 0
[3,1] => [[1,3,4],[2]] => [1,3] => 2
[2,2] => [[1,2],[3,4]] => [2,2] => 0
[2,1,1] => [[1,4],[2],[3]] => [1,1,2] => 1
[1,1,1,1] => [[1],[2],[3],[4]] => [1,1,1,1] => 0
[5] => [[1,2,3,4,5]] => [5] => 0
[4,1] => [[1,3,4,5],[2]] => [1,4] => 3
[3,2] => [[1,2,5],[3,4]] => [2,3] => 1
[3,1,1] => [[1,4,5],[2],[3]] => [1,1,3] => 2
[2,2,1] => [[1,3],[2,5],[4]] => [1,2,2] => 1
[2,1,1,1] => [[1,5],[2],[3],[4]] => [1,1,1,2] => 1
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 0
[6] => [[1,2,3,4,5,6]] => [6] => 0
[5,1] => [[1,3,4,5,6],[2]] => [1,5] => 4
[4,2] => [[1,2,5,6],[3,4]] => [2,4] => 2
[4,1,1] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[3,3] => [[1,2,3],[4,5,6]] => [3,3] => 0
[3,2,1] => [[1,3,6],[2,5],[4]] => [1,2,3] => 2
[3,1,1,1] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 2
[2,2,2] => [[1,2],[3,4],[5,6]] => [2,2,2] => 0
[2,2,1,1] => [[1,4],[2,6],[3],[5]] => [1,1,2,2] => 1
[2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 1
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 0
[7] => [[1,2,3,4,5,6,7]] => [7] => 0
[6,1] => [[1,3,4,5,6,7],[2]] => [1,6] => 5
[5,2] => [[1,2,5,6,7],[3,4]] => [2,5] => 3
[5,1,1] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 4
[4,3] => [[1,2,3,7],[4,5,6]] => [3,4] => 1
[4,2,1] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 3
[4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 3
[3,3,1] => [[1,3,4],[2,6,7],[5]] => [1,3,3] => 2
[3,2,2] => [[1,2,7],[3,4],[5,6]] => [2,2,3] => 1
[3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 2
[3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 2
[2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [1,2,2,2] => 1
[2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => 1
[2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 1
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => 0
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Description
The descent variation of a composition.
Defined in [1].
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a 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 $i$.