Identifier
Values
[1] => [[1]] => {{1}} => [1] => 1
[2] => [[1,2]] => {{1,2}} => [2,1] => 2
[1,1] => [[1],[2]] => {{1},{2}} => [1,2] => 1
[3] => [[1,2,3]] => {{1,2,3}} => [2,3,1] => 3
[2,1] => [[1,3],[2]] => {{1,3},{2}} => [3,2,1] => 2
[1,1,1] => [[1],[2],[3]] => {{1},{2},{3}} => [1,2,3] => 1
[4] => [[1,2,3,4]] => {{1,2,3,4}} => [2,3,4,1] => 4
[3,1] => [[1,3,4],[2]] => {{1,3,4},{2}} => [3,2,4,1] => 3
[2,2] => [[1,2],[3,4]] => {{1,2},{3,4}} => [2,1,4,3] => 2
[2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => [4,2,3,1] => 2
[1,1,1,1] => [[1],[2],[3],[4]] => {{1},{2},{3},{4}} => [1,2,3,4] => 1
[5] => [[1,2,3,4,5]] => {{1,2,3,4,5}} => [2,3,4,5,1] => 5
[4,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => [3,2,4,5,1] => 4
[3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => [2,5,4,3,1] => 6
[3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 3
[2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 2
[2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 2
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 1
[6] => [[1,2,3,4,5,6]] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 6
[5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 5
[4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 4
[4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 4
[3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 3
[3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 6
[3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 3
[2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 2
[2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 2
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => 1
[7] => [[1,2,3,4,5,6,7]] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 7
[6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => 6
[5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => [2,5,4,3,6,7,1] => 10
[5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => 5
[4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => 12
[4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => [3,5,6,4,2,7,1] => 4
[4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => 4
[3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => 6
[3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => 6
[3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => 3
[2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => 2
[2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => 2
[2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => 2
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => {{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => 1
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Description
The order of a permutation.
$\operatorname{ord}(\pi)$ is given by the minimial $k$ for which $\pi^k$ is the identity permutation.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
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
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.