Identifier
Values
[2] => [[1,2]] => {{1,2}} => [2,1] => 1
[1,1] => [[1],[2]] => {{1},{2}} => [1,2] => 1
[3] => [[1,2,3]] => {{1,2,3}} => [2,3,1] => 2
[2,1] => [[1,3],[2]] => {{1,3},{2}} => [3,2,1] => 3
[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] => 6
[3,1] => [[1,3,4],[2]] => {{1,3,4},{2}} => [3,2,4,1] => 8
[2,2] => [[1,2],[3,4]] => {{1,2},{3,4}} => [2,1,4,3] => 3
[2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => [4,2,3,1] => 6
[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] => 24
[4,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => [3,2,4,5,1] => 30
[3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => [2,5,4,3,1] => 20
[3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 20
[2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 15
[2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 10
[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] => 120
[5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 144
[4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 90
[4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 90
[3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 40
[3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 120
[3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 40
[2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 15
[2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 45
[2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 15
[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
[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 size of the conjugacy class of a permutation.
Two permutations are conjugate if and only if they have the same cycle type, this statistic is then computed as described in St000182The number of permutations whose cycle type is the given integer partition..
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.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.