- FindStat

Identifier

Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions

Images

[1] => [[1]] => [1] => {{1}}

[2] => [[1,2]] => [1,2] => {{1},{2}}

[1,1] => [[1],[2]] => [2,1] => {{1,2}}

[3] => [[1,2,3]] => [1,2,3] => {{1},{2},{3}}

[2,1] => [[1,3],[2]] => [2,1,3] => {{1,2},{3}}

[1,1,1] => [[1],[2],[3]] => [3,2,1] => {{1,3},{2}}

[4] => [[1,2,3,4]] => [1,2,3,4] => {{1},{2},{3},{4}}

[3,1] => [[1,3,4],[2]] => [2,1,3,4] => {{1,2},{3},{4}}

[2,2] => [[1,2],[3,4]] => [3,4,1,2] => {{1,3},{2,4}}

[2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => {{1,3},{2},{4}}

[1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => {{1,4},{2,3}}

[5] => [[1,2,3,4,5]] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}}

[4,1] => [[1,3,4,5],[2]] => [2,1,3,4,5] => {{1,2},{3},{4},{5}}

[3,2] => [[1,2,5],[3,4]] => [3,4,1,2,5] => {{1,3},{2,4},{5}}

[3,1,1] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => {{1,3},{2},{4},{5}}

[2,2,1] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => {{1,4},{2},{3,5}}

[2,1,1,1] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => {{1,4},{2,3},{5}}

[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => {{1,5},{2,4},{3}}

[6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}}

[5,1] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}}

[4,2] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}}

[4,1,1] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}}

[3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}}

[3,2,1] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => {{1,4},{2},{3,5},{6}}

[3,1,1,1] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}}

[2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}}

[2,2,1,1] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => {{1,5},{2,3},{4,6}}

[2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}}

[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}}

[7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}}

[6,1] => [[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}}

[5,2] => [[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}}

[5,1,1] => [[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}}

[4,3] => [[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}}

[4,2,1] => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => {{1,4},{2},{3,5},{6},{7}}

[4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}}

[3,3,1] => [[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => {{1,5},{2},{3,6},{4,7}}

[3,2,2] => [[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => {{1,5},{2,6},{3},{4},{7}}

[3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => {{1,5},{2,3},{4,6},{7}}

[3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}}

[2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => {{1,6},{2,4},{3,7},{5}}

[2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => {{1,6},{2,4},{3},{5,7}}

[2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}}

[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}}

[8] => [[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}}

[7,1] => [[1,3,4,5,6,7,8],[2]] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}}

[6,2] => [[1,2,5,6,7,8],[3,4]] => [3,4,1,2,5,6,7,8] => {{1,3},{2,4},{5},{6},{7},{8}}

[6,1,1] => [[1,4,5,6,7,8],[2],[3]] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}}

[5,3] => [[1,2,3,7,8],[4,5,6]] => [4,5,6,1,2,3,7,8] => {{1,4},{2,5},{3,6},{7},{8}}

[5,2,1] => [[1,3,6,7,8],[2,5],[4]] => [4,2,5,1,3,6,7,8] => {{1,4},{2},{3,5},{6},{7},{8}}

[5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => [4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}}

[4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => {{1,5},{2,6},{3,7},{4,8}}

[4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [5,2,6,7,1,3,4,8] => {{1,5},{2},{3,6},{4,7},{8}}

[4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [5,6,3,4,1,2,7,8] => {{1,5},{2,6},{3},{4},{7},{8}}

[4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8] => {{1,5},{2,3},{4,6},{7},{8}}

[4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8] => {{1,5},{2,4},{3},{6},{7},{8}}

[3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5] => {{1,6},{2,7},{3},{4},{5,8}}

[3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5] => {{1,6},{2,3},{4,7},{5,8}}

[3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => {{1,6},{2,4},{3,7},{5},{8}}

[3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8] => {{1,6},{2,4},{3},{5,7},{8}}

[3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8] => {{1,6},{2,5},{3,4},{7},{8}}

[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => {{1,7},{2,8},{3,5},{4,6}}

[2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4] => {{1,7},{2,5},{3},{4,8},{6}}

[2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6] => {{1,7},{2,5},{3,4},{6,8}}

[2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => {{1,7},{2,6},{3,5},{4},{8}}

[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}}

[9] => [[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}

[8,1] => [[1,3,4,5,6,7,8,9],[2]] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}}

[7,2] => [[1,2,5,6,7,8,9],[3,4]] => [3,4,1,2,5,6,7,8,9] => {{1,3},{2,4},{5},{6},{7},{8},{9}}

[7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}}

[6,3] => [[1,2,3,7,8,9],[4,5,6]] => [4,5,6,1,2,3,7,8,9] => {{1,4},{2,5},{3,6},{7},{8},{9}}

[6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => [4,2,5,1,3,6,7,8,9] => {{1,4},{2},{3,5},{6},{7},{8},{9}}

[6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9] => {{1,4},{2,3},{5},{6},{7},{8},{9}}

[5,4] => [[1,2,3,4,9],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9] => {{1,5},{2,6},{3,7},{4,8},{9}}

[5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => [5,2,6,7,1,3,4,8,9] => {{1,5},{2},{3,6},{4,7},{8},{9}}

[5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9] => {{1,5},{2,6},{3},{4},{7},{8},{9}}

[5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8,9] => {{1,5},{2,3},{4,6},{7},{8},{9}}

[5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9] => {{1,5},{2,4},{3},{6},{7},{8},{9}}

[4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => [6,2,7,8,9,1,3,4,5] => {{1,6},{2},{3,7},{4,8},{5,9}}

[4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9] => {{1,6},{2,7},{3},{4},{5,8},{9}}

[4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5,9] => {{1,6},{2,3},{4,7},{5,8},{9}}

[4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8,9] => {{1,6},{2,4},{3,7},{5},{8},{9}}

[4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8,9] => {{1,6},{2,4},{3},{5,7},{8},{9}}

[4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9] => {{1,6},{2,5},{3,4},{7},{8},{9}}

[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => {{1,7},{2,8},{3,9},{4},{5},{6}}

[3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => [7,4,8,2,5,9,1,3,6] => {{1,7},{2,4},{3,8},{5},{6,9}}

[3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => [7,4,3,2,8,9,1,5,6] => {{1,7},{2,4},{3},{5,8},{6,9}}

[3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9] => {{1,7},{2,8},{3,5},{4,6},{9}}

[3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4,9] => {{1,7},{2,5},{3},{4,8},{6},{9}}

[3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6,9] => {{1,7},{2,5},{3,4},{6,8},{9}}

[3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9] => {{1,7},{2,6},{3,5},{4},{8},{9}}

[2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3] => {{1,8},{2,6},{3,9},{4},{5,7}}

[2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => [8,6,4,3,9,2,7,1,5] => {{1,8},{2,6},{3,4},{5,9},{7}}

[2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7] => {{1,8},{2,6},{3,5},{4},{7,9}}

[2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => {{1,8},{2,7},{3,6},{4,5},{9}}

[1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => {{1,9},{2,8},{3,7},{4,6},{5}}

[10] => [[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}

[9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}

[8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [3,4,1,2,5,6,7,8,9,10] => {{1,3},{2,4},{5},{6},{7},{8},{9},{10}}

[8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}

[7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => [4,5,6,1,2,3,7,8,9,10] => {{1,4},{2,5},{3,6},{7},{8},{9},{10}}

>>> Load all 139 entries. <<<

[7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => [4,2,5,1,3,6,7,8,9,10] => {{1,4},{2},{3,5},{6},{7},{8},{9},{10}}

[7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9,10] => {{1,4},{2,3},{5},{6},{7},{8},{9},{10}}

[6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9,10] => {{1,5},{2,6},{3,7},{4,8},{9},{10}}

[6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => [5,2,6,7,1,3,4,8,9,10] => {{1,5},{2},{3,6},{4,7},{8},{9},{10}}

[6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9,10] => {{1,5},{2,6},{3},{4},{7},{8},{9},{10}}

[6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8,9,10] => {{1,5},{2,3},{4,6},{7},{8},{9},{10}}

[6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9,10] => {{1,5},{2,4},{3},{6},{7},{8},{9},{10}}

[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => {{1,6},{2,7},{3,8},{4,9},{5,10}}

[5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => [6,2,7,8,9,1,3,4,5,10] => {{1,6},{2},{3,7},{4,8},{5,9},{10}}

[5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9,10] => {{1,6},{2,7},{3},{4},{5,8},{9},{10}}

[5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5,9,10] => {{1,6},{2,3},{4,7},{5,8},{9},{10}}

[5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8,9,10] => {{1,6},{2,4},{3,7},{5},{8},{9},{10}}

[5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8,9,10] => {{1,6},{2,4},{3},{5,7},{8},{9},{10}}

[5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9,10] => {{1,6},{2,5},{3,4},{7},{8},{9},{10}}

[4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => [7,8,3,4,9,10,1,2,5,6] => {{1,7},{2,8},{3},{4},{5,9},{6,10}}

[4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => [7,3,2,8,9,10,1,4,5,6] => {{1,7},{2,3},{4,8},{5,9},{6,10}}

[4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3,10] => {{1,7},{2,8},{3,9},{4},{5},{6},{10}}

[4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => [7,4,8,2,5,9,1,3,6,10] => {{1,7},{2,4},{3,8},{5},{6,9},{10}}

[4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => [7,4,3,2,8,9,1,5,6,10] => {{1,7},{2,4},{3},{5,8},{6,9},{10}}

[4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9,10] => {{1,7},{2,8},{3,5},{4,6},{9},{10}}

[4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4,9,10] => {{1,7},{2,5},{3},{4,8},{6},{9},{10}}

[4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6,9,10] => {{1,7},{2,5},{3,4},{6,8},{9},{10}}

[4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9,10] => {{1,7},{2,6},{3,5},{4},{8},{9},{10}}

[3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => [8,5,9,10,2,6,7,1,3,4] => {{1,8},{2,5},{3,9},{4,10},{6},{7}}

[3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => [8,9,5,6,3,4,10,1,2,7] => {{1,8},{2,9},{3,5},{4,6},{7,10}}

[3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => [8,5,3,9,2,6,10,1,4,7] => {{1,8},{2,5},{3},{4,9},{6},{7,10}}

[3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => [8,5,4,3,2,9,10,1,6,7] => {{1,8},{2,5},{3,4},{6,9},{7,10}}

[3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3,10] => {{1,8},{2,6},{3,9},{4},{5,7},{10}}

[3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => [8,6,4,3,9,2,7,1,5,10] => {{1,8},{2,6},{3,4},{5,9},{7},{10}}

[3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7,10] => {{1,8},{2,6},{3,5},{4},{7,9},{10}}

[3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9,10] => {{1,8},{2,7},{3,6},{4,5},{9},{10}}

[2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => {{1,9},{2,10},{3,7},{4,8},{5},{6}}

[2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => [9,7,5,10,3,8,2,6,1,4] => {{1,9},{2,7},{3,5},{4,10},{6,8}}

[2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => [9,7,5,4,3,10,2,8,1,6] => {{1,9},{2,7},{3,5},{4},{6,10},{8}}

[2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,10,1,8] => {{1,9},{2,7},{3,6},{4,5},{8,10}}

[2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => {{1,9},{2,8},{3,7},{4,6},{5},{10}}

[1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => {{1,10},{2,9},{3,8},{4,7},{5,6}}

[6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [7,8,9,10,11,12,1,2,3,4,5,6] => {{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}

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

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.

Map

weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs

$(i, \pi(i))$ with

$i\leq\pi(i)$ .