Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Images
[1] => [[1]] => [1] => [1]
[2] => [[1,2]] => [1,2] => [1,2]
[1,1] => [[1],[2]] => [2,1] => [2,1]
[3] => [[1,2,3]] => [1,2,3] => [1,2,3]
[2,1] => [[1,2],[3]] => [3,1,2] => [2,3,1]
[1,1,1] => [[1],[2],[3]] => [3,2,1] => [3,2,1]
[4] => [[1,2,3,4]] => [1,2,3,4] => [1,2,3,4]
[3,1] => [[1,2,3],[4]] => [4,1,2,3] => [2,3,4,1]
[2,2] => [[1,2],[3,4]] => [3,4,1,2] => [3,4,1,2]
[2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => [3,4,2,1]
[1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => [4,3,2,1]
[5] => [[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5]
[4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1]
[3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => [3,4,5,1,2]
[3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1]
[2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => [4,5,2,3,1]
[2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [4,5,3,2,1]
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5,4,3,2,1]
[6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,2,3,4,5,6]
[5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [2,3,4,5,6,1]
[4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [3,4,5,6,1,2]
[4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [3,4,5,6,2,1]
[3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [4,5,6,1,2,3]
[3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [4,5,6,2,3,1]
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [4,5,6,3,2,1]
[2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [5,6,3,4,1,2]
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [5,6,3,4,2,1]
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [5,6,4,3,2,1]
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1]
[5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [3,4,5,6,7,1,2]
[5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1]
[4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [4,5,6,7,1,2,3]
[4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [4,5,6,7,2,3,1]
[4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [4,5,6,7,3,2,1]
[3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [5,6,7,2,3,4,1]
[3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [5,6,7,3,4,1,2]
[3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [5,6,7,3,4,2,1]
[3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [5,6,7,4,3,2,1]
[2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [6,7,4,5,2,3,1]
[2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [6,7,4,5,3,2,1]
[2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [6,7,5,4,3,2,1]
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[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] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1]
[6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [3,4,5,6,7,8,1,2]
[6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [3,4,5,6,7,8,2,1]
[5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => [4,5,6,7,8,1,2,3]
[5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [4,5,6,7,8,2,3,1]
[5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [4,5,6,7,8,3,2,1]
[4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [5,6,7,8,1,2,3,4]
[4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => [5,6,7,8,2,3,4,1]
[4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [5,6,7,8,3,4,1,2]
[4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [5,6,7,8,3,4,2,1]
[4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [5,6,7,8,4,3,2,1]
[3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => [6,7,8,3,4,5,1,2]
[3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => [6,7,8,3,4,5,2,1]
[3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => [6,7,8,4,5,2,3,1]
[3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => [6,7,8,4,5,3,2,1]
[3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [6,7,8,5,4,3,2,1]
[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [7,8,5,6,3,4,1,2]
[2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => [7,8,5,6,3,4,2,1]
[2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => [7,8,5,6,4,3,2,1]
[2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [7,8,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[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] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1]
[7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [3,4,5,6,7,8,9,1,2]
[7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [3,4,5,6,7,8,9,2,1]
[6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [4,5,6,7,8,9,1,2,3]
[6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [4,5,6,7,8,9,2,3,1]
[6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [4,5,6,7,8,9,3,2,1]
[5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => [5,6,7,8,9,1,2,3,4]
[5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => [5,6,7,8,9,2,3,4,1]
[5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => [5,6,7,8,9,3,4,1,2]
[5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [5,6,7,8,9,3,4,2,1]
[5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [5,6,7,8,9,4,3,2,1]
[4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => [6,7,8,9,2,3,4,5,1]
[4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => [6,7,8,9,3,4,5,1,2]
[4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => [6,7,8,9,3,4,5,2,1]
[4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => [6,7,8,9,4,5,2,3,1]
[4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [6,7,8,9,4,5,3,2,1]
[4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [6,7,8,9,5,4,3,2,1]
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => [7,8,9,4,5,6,1,2,3]
[3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => [7,8,9,4,5,6,2,3,1]
[3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => [7,8,9,4,5,6,3,2,1]
[3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => [7,8,9,5,6,3,4,1,2]
[3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => [7,8,9,5,6,3,4,2,1]
[3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => [7,8,9,5,6,4,3,2,1]
[3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [7,8,9,6,5,4,3,2,1]
[2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => [8,9,6,7,4,5,2,3,1]
[2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => [8,9,6,7,4,5,3,2,1]
[2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => [8,9,6,7,5,4,3,2,1]
[2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [8,9,7,6,5,4,3,2,1]
[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] => [9,8,7,6,5,4,3,2,1]
[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] => [[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1]
[8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => [3,4,5,6,7,8,9,10,1,2]
[8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [3,4,5,6,7,8,9,10,2,1]
[7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => [4,5,6,7,8,9,10,1,2,3]
>>> Load all 198 entries. <<<
[7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => [4,5,6,7,8,9,10,2,3,1]
[7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => [4,5,6,7,8,9,10,3,2,1]
[6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => [5,6,7,8,9,10,1,2,3,4]
[6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => [5,6,7,8,9,10,2,3,4,1]
[6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => [5,6,7,8,9,10,3,4,1,2]
[6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => [5,6,7,8,9,10,3,4,2,1]
[6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => [5,6,7,8,9,10,4,3,2,1]
[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [6,7,8,9,10,1,2,3,4,5]
[5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => [6,7,8,9,10,2,3,4,5,1]
[5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => [6,7,8,9,10,3,4,5,1,2]
[5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => [6,7,8,9,10,3,4,5,2,1]
[5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => [6,7,8,9,10,4,5,2,3,1]
[5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => [6,7,8,9,10,4,5,3,2,1]
[5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => [6,7,8,9,10,5,4,3,2,1]
[4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => [7,8,9,10,3,4,5,6,1,2]
[4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => [7,8,9,10,3,4,5,6,2,1]
[4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => [7,8,9,10,4,5,6,1,2,3]
[4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => [7,8,9,10,4,5,6,2,3,1]
[4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => [7,8,9,10,4,5,6,3,2,1]
[4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => [7,8,9,10,5,6,3,4,1,2]
[4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => [7,8,9,10,5,6,3,4,2,1]
[4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => [7,8,9,10,5,6,4,3,2,1]
[4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => [7,8,9,10,6,5,4,3,2,1]
[3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => [8,9,10,5,6,7,2,3,4,1]
[3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => [8,9,10,5,6,7,3,4,1,2]
[3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => [8,9,10,5,6,7,3,4,2,1]
[3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => [8,9,10,5,6,7,4,3,2,1]
[3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => [8,9,10,6,7,4,5,2,3,1]
[3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => [8,9,10,6,7,4,5,3,2,1]
[3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => [8,9,10,6,7,5,4,3,2,1]
[3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => [8,9,10,7,6,5,4,3,2,1]
[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] => [9,10,7,8,5,6,3,4,1,2]
[2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => [9,10,7,8,5,6,3,4,2,1]
[2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => [9,10,7,8,5,6,4,3,2,1]
[2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => [9,10,7,8,6,5,4,3,2,1]
[2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => [9,10,8,7,6,5,4,3,2,1]
[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] => [10,9,8,7,6,5,4,3,2,1]
[5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => [10,11,6,7,8,9,1,2,3,4,5] => [7,8,9,10,11,3,4,5,6,1,2]
[5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => [11,10,6,7,8,9,1,2,3,4,5] => [7,8,9,10,11,3,4,5,6,2,1]
[5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => [9,10,11,6,7,8,1,2,3,4,5] => [7,8,9,10,11,4,5,6,1,2,3]
[5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => [11,9,10,6,7,8,1,2,3,4,5] => [7,8,9,10,11,4,5,6,2,3,1]
[5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => [11,10,9,6,7,8,1,2,3,4,5] => [7,8,9,10,11,4,5,6,3,2,1]
[5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => [10,11,8,9,6,7,1,2,3,4,5] => [7,8,9,10,11,5,6,3,4,1,2]
[5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => [11,10,8,9,6,7,1,2,3,4,5] => [7,8,9,10,11,5,6,3,4,2,1]
[4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => [9,10,11,5,6,7,8,1,2,3,4] => [8,9,10,11,4,5,6,7,1,2,3]
[4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => [11,9,10,5,6,7,8,1,2,3,4] => [8,9,10,11,4,5,6,7,2,3,1]
[4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => [11,10,9,5,6,7,8,1,2,3,4] => [8,9,10,11,4,5,6,7,3,2,1]
[4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => [11,8,9,10,5,6,7,1,2,3,4] => [8,9,10,11,5,6,7,2,3,4,1]
[4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => [10,11,8,9,5,6,7,1,2,3,4] => [8,9,10,11,5,6,7,3,4,1,2]
[4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => [11,10,8,9,5,6,7,1,2,3,4] => [8,9,10,11,5,6,7,3,4,2,1]
[4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => [11,9,10,7,8,5,6,1,2,3,4] => [8,9,10,11,6,7,4,5,2,3,1]
[3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => [10,11,7,8,9,4,5,6,1,2,3] => [9,10,11,6,7,8,3,4,5,1,2]
[3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => [11,10,7,8,9,4,5,6,1,2,3] => [9,10,11,6,7,8,3,4,5,2,1]
[3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => [11,9,10,7,8,4,5,6,1,2,3] => [9,10,11,6,7,8,4,5,2,3,1]
[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] => [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] => [7,8,9,10,11,12,1,2,3,4,5,6]
[6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => [11,12,7,8,9,10,1,2,3,4,5,6] => [7,8,9,10,11,12,3,4,5,6,1,2]
[5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => [10,11,12,6,7,8,9,1,2,3,4,5] => [8,9,10,11,12,4,5,6,7,1,2,3]
[5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => [12,10,11,6,7,8,9,1,2,3,4,5] => [8,9,10,11,12,4,5,6,7,2,3,1]
[5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => [12,11,10,6,7,8,9,1,2,3,4,5] => [8,9,10,11,12,4,5,6,7,3,2,1]
[5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => [12,9,10,11,6,7,8,1,2,3,4,5] => [8,9,10,11,12,5,6,7,2,3,4,1]
[5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => [11,12,9,10,6,7,8,1,2,3,4,5] => [8,9,10,11,12,5,6,7,3,4,1,2]
[5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => [12,11,9,10,6,7,8,1,2,3,4,5] => [8,9,10,11,12,5,6,7,3,4,2,1]
[5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => [12,10,11,8,9,6,7,1,2,3,4,5] => [8,9,10,11,12,6,7,4,5,2,3,1]
[4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => [12,9,10,11,5,6,7,8,1,2,3,4] => [9,10,11,12,5,6,7,8,2,3,4,1]
[4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [11,12,9,10,5,6,7,8,1,2,3,4] => [9,10,11,12,5,6,7,8,3,4,1,2]
[4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => [12,11,9,10,5,6,7,8,1,2,3,4] => [9,10,11,12,5,6,7,8,3,4,2,1]
[4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => [11,12,8,9,10,5,6,7,1,2,3,4] => [9,10,11,12,6,7,8,3,4,5,1,2]
[4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => [12,11,8,9,10,5,6,7,1,2,3,4] => [9,10,11,12,6,7,8,3,4,5,2,1]
[4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => [12,10,11,8,9,5,6,7,1,2,3,4] => [9,10,11,12,6,7,8,4,5,2,3,1]
[4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,1,2,3,4] => [9,10,11,12,7,8,5,6,3,4,1,2]
[3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => [12,10,11,7,8,9,4,5,6,1,2,3] => [10,11,12,7,8,9,4,5,6,2,3,1]
[3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [12,11,9,10,7,8,4,5,6,1,2,3] => [10,11,12,7,8,9,5,6,3,4,2,1]
[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] => [11,12,9,10,7,8,5,6,3,4,1,2]
[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] => [12,11,10,9,8,7,6,5,4,3,2,1]
[5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => [13,10,11,12,6,7,8,9,1,2,3,4,5] => [9,10,11,12,13,5,6,7,8,2,3,4,1]
[5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => [12,13,10,11,6,7,8,9,1,2,3,4,5] => [9,10,11,12,13,5,6,7,8,3,4,1,2]
[5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => [13,12,10,11,6,7,8,9,1,2,3,4,5] => [9,10,11,12,13,5,6,7,8,3,4,2,1]
[5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => [12,13,9,10,11,6,7,8,1,2,3,4,5] => [9,10,11,12,13,6,7,8,3,4,5,1,2]
[5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => [13,12,9,10,11,6,7,8,1,2,3,4,5] => [9,10,11,12,13,6,7,8,3,4,5,2,1]
[5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => [13,11,12,9,10,6,7,8,1,2,3,4,5] => [9,10,11,12,13,6,7,8,4,5,2,3,1]
[4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => [12,13,9,10,11,5,6,7,8,1,2,3,4] => [10,11,12,13,6,7,8,9,3,4,5,1,2]
[4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => [13,12,9,10,11,5,6,7,8,1,2,3,4] => [10,11,12,13,6,7,8,9,3,4,5,2,1]
[4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => [13,11,12,9,10,5,6,7,8,1,2,3,4] => [10,11,12,13,6,7,8,9,4,5,2,3,1]
[4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => [13,11,12,8,9,10,5,6,7,1,2,3,4] => [10,11,12,13,7,8,9,4,5,6,2,3,1]
[7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => [8,9,10,11,12,13,14,1,2,3,4,5,6,7] => [8,9,10,11,12,13,14,1,2,3,4,5,6,7]
[5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => [13,14,10,11,12,6,7,8,9,1,2,3,4,5] => [10,11,12,13,14,6,7,8,9,3,4,5,1,2]
[5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => [14,13,10,11,12,6,7,8,9,1,2,3,4,5] => [10,11,12,13,14,6,7,8,9,3,4,5,2,1]
[5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => [14,12,13,10,11,6,7,8,9,1,2,3,4,5] => [10,11,12,13,14,6,7,8,9,4,5,2,3,1]
[5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => [14,12,13,9,10,11,6,7,8,1,2,3,4,5] => [10,11,12,13,14,7,8,9,4,5,6,2,3,1]
[4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => [14,12,13,9,10,11,5,6,7,8,1,2,3,4] => [11,12,13,14,7,8,9,10,4,5,6,2,3,1]
[2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]] => [13,14,11,12,9,10,7,8,5,6,3,4,1,2] => [13,14,11,12,9,10,7,8,5,6,3,4,1,2]
[5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => [15,13,14,10,11,12,6,7,8,9,1,2,3,4,5] => [11,12,13,14,15,7,8,9,10,4,5,6,2,3,1]
[2,2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16]] => [15,16,13,14,11,12,9,10,7,8,5,6,3,4,1,2] => [15,16,13,14,11,12,9,10,7,8,5,6,3,4,1,2]
[] => [] => [] => []
[2,2,2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18]] => [17,18,15,16,13,14,11,12,9,10,7,8,5,6,3,4,1,2] => [17,18,15,16,13,14,11,12,9,10,7,8,5,6,3,4,1,2]
[2,2,2,2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18],[19,20]] => [19,20,17,18,15,16,13,14,11,12,9,10,7,8,5,6,3,4,1,2] => [19,20,17,18,15,16,13,14,11,12,9,10,7,8,5,6,3,4,1,2]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
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
inverse
Description
Sends a permutation to its inverse.