- FindStat

Identifier

Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux

Images

[1] => [[1]] => [1] => [1] => [[1]]

[2] => [[1,2]] => [1,2] => [2,1] => [[1],[2]]

[1,1] => [[1],[2]] => [2,1] => [1,2] => [[1,2]]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 143 entries. <<<

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

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

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

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

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

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

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

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

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

[] => [] => [] => [] => []

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

complement

Description

Sents a permutation to its complement.
The complement of a permutation

$\sigma$ of length

$n$ is the permutation

$\tau$ with

$\tau(i) = n+1-\sigma(i)$

Map

Robinson-Schensted recording tableau

Description

Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length

$n$ and pairs of standard Young tableaux of the same shape and of size

$n$ , see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.