Processing math: 100%

Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
[1] => [[1]] => [1] => [1] => [1]
[2] => [[1,2]] => [1,2] => [1,2] => [2]
[1,1] => [[1],[2]] => [2,1] => [2,1] => [1,1]
[3] => [[1,2,3]] => [1,2,3] => [1,2,3] => [3]
[2,1] => [[1,2],[3]] => [3,1,2] => [1,3,2] => [2,1]
[1,1,1] => [[1],[2],[3]] => [3,2,1] => [3,2,1] => [1,1,1]
[4] => [[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [4]
[3,1] => [[1,2,3],[4]] => [4,1,2,3] => [1,2,4,3] => [3,1]
[2,2] => [[1,2],[3,4]] => [3,4,1,2] => [1,4,2,3] => [2,2]
[2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => [1,4,3,2] => [2,1,1]
[1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1]
[5] => [[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [5]
[4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [1,2,3,5,4] => [4,1]
[3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => [1,2,5,3,4] => [3,2]
[3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [1,2,5,4,3] => [3,1,1]
[2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => [1,5,2,4,3] => [2,2,1]
[2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [1,5,4,3,2] => [2,1,1,1]
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1]
[6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [6]
[5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => [5,1]
[4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [1,2,3,6,4,5] => [4,2]
[4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => [4,1,1]
[3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [1,2,6,3,4,5] => [3,3]
[3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [1,2,6,3,5,4] => [3,2,1]
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => [3,1,1,1]
[2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [1,6,2,5,3,4] => [2,2,2]
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [1,6,2,5,4,3] => [2,2,1,1]
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [2,1,1,1,1]
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1]
[7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [7]
[6,1] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => [6,1]
[5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [1,2,3,4,7,5,6] => [5,2]
[5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => [5,1,1]
[4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [1,2,3,7,4,5,6] => [4,3]
[4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,2,3,7,4,6,5] => [4,2,1]
[4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => [4,1,1,1]
[3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [1,2,7,3,4,6,5] => [3,3,1]
[3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [1,2,7,3,6,4,5] => [3,2,2]
[3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [1,2,7,3,6,5,4] => [3,2,1,1]
[3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => [3,1,1,1,1]
[2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [1,7,2,6,3,5,4] => [2,2,2,1]
[2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [1,7,2,6,5,4,3] => [2,2,1,1,1]
[2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => [2,1,1,1,1,1]
[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] => [1,1,1,1,1,1,1]
[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] => [8]
[7,1] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => [7,1]
[6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,8,6,7] => [6,2]
[6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,8,7,6] => [6,1,1]
[5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => [1,2,3,4,8,5,6,7] => [5,3]
[5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [1,2,3,4,8,5,7,6] => [5,2,1]
[5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [1,2,3,4,8,7,6,5] => [5,1,1,1]
[4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [1,2,3,8,4,5,6,7] => [4,4]
[4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => [1,2,3,8,4,5,7,6] => [4,3,1]
[4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [1,2,3,8,4,7,5,6] => [4,2,2]
[4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [1,2,3,8,4,7,6,5] => [4,2,1,1]
[4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [1,2,3,8,7,6,5,4] => [4,1,1,1,1]
[3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => [1,2,8,3,4,7,5,6] => [3,3,2]
[3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => [1,2,8,3,4,7,6,5] => [3,3,1,1]
[3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => [1,2,8,3,7,4,6,5] => [3,2,2,1]
[3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => [1,2,8,3,7,6,5,4] => [3,2,1,1,1]
[3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [1,2,8,7,6,5,4,3] => [3,1,1,1,1,1]
[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [1,8,2,7,3,6,4,5] => [2,2,2,2]
[2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => [1,8,2,7,3,6,5,4] => [2,2,2,1,1]
[2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => [1,8,2,7,6,5,4,3] => [2,2,1,1,1,1]
[2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [1,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1]
[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] => [1,1,1,1,1,1,1,1]
[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] => [9]
[8,1] => [[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => [8,1]
[7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,9,7,8] => [7,2]
[7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,9,8,7] => [7,1,1]
[6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,9,6,7,8] => [6,3]
[6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [1,2,3,4,5,9,6,8,7] => [6,2,1]
[6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,9,8,7,6] => [6,1,1,1]
[5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => [1,2,3,4,9,5,6,7,8] => [5,4]
[5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => [1,2,3,4,9,5,6,8,7] => [5,3,1]
[5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => [1,2,3,4,9,5,8,6,7] => [5,2,2]
[5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [1,2,3,4,9,5,8,7,6] => [5,2,1,1]
[5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,9,8,7,6,5] => [5,1,1,1,1]
[4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => [1,2,3,9,4,5,6,8,7] => [4,4,1]
[4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => [1,2,3,9,4,5,8,6,7] => [4,3,2]
[4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => [1,2,3,9,4,5,8,7,6] => [4,3,1,1]
[4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => [1,2,3,9,4,8,5,7,6] => [4,2,2,1]
[4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [1,2,3,9,4,8,7,6,5] => [4,2,1,1,1]
[4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [1,2,3,9,8,7,6,5,4] => [4,1,1,1,1,1]
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => [1,2,9,3,4,8,5,6,7] => [3,3,3]
[3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => [1,2,9,3,4,8,5,7,6] => [3,3,2,1]
[3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => [1,2,9,3,4,8,7,6,5] => [3,3,1,1,1]
[3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => [1,2,9,3,8,4,7,5,6] => [3,2,2,2]
[3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => [1,2,9,3,8,4,7,6,5] => [3,2,2,1,1]
[3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => [1,2,9,3,8,7,6,5,4] => [3,2,1,1,1,1]
[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] => [1,2,9,8,7,6,5,4,3] => [3,1,1,1,1,1,1]
[2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => [1,9,2,8,3,7,4,6,5] => [2,2,2,2,1]
[2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => [1,9,2,8,3,7,6,5,4] => [2,2,2,1,1,1]
[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] => [1,9,2,8,7,6,5,4,3] => [2,2,1,1,1,1,1]
[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] => [1,9,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1,1]
[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] => [1,1,1,1,1,1,1,1,1]
[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] => [10]
[9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,9] => [9,1]
[8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,10,8,9] => [8,2]
[8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,10,9,8] => [8,1,1]
[7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,10,7,8,9] => [7,3]
>>> Load all 146 entries. <<<
[7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,10,7,9,8] => [7,2,1]
[7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,10,9,8,7] => [7,1,1,1]
[6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => [1,2,3,4,5,10,6,7,8,9] => [6,4]
[6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,10,6,7,9,8] => [6,3,1]
[6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => [1,2,3,4,5,10,6,9,7,8] => [6,2,2]
[6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => [1,2,3,4,5,10,6,9,8,7] => [6,2,1,1]
[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] => [1,2,3,4,5,10,9,8,7,6] => [6,1,1,1,1]
[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,10,5,6,7,8,9] => [5,5]
[5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => [1,2,3,4,10,5,6,7,9,8] => [5,4,1]
[5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => [1,2,3,4,10,5,6,9,7,8] => [5,3,2]
[5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => [1,2,3,4,10,5,6,9,8,7] => [5,3,1,1]
[5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => [1,2,3,4,10,5,9,6,8,7] => [5,2,2,1]
[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] => [1,2,3,4,10,5,9,8,7,6] => [5,2,1,1,1]
[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] => [1,2,3,4,10,9,8,7,6,5] => [5,1,1,1,1,1]
[4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => [1,2,3,10,4,5,6,9,7,8] => [4,4,2]
[4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => [1,2,3,10,4,5,6,9,8,7] => [4,4,1,1]
[4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => [1,2,3,10,4,5,9,6,7,8] => [4,3,3]
[4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => [1,2,3,10,4,5,9,6,8,7] => [4,3,2,1]
[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] => [1,2,3,10,4,5,9,8,7,6] => [4,3,1,1,1]
[4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => [1,2,3,10,4,9,5,8,6,7] => [4,2,2,2]
[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] => [1,2,3,10,4,9,5,8,7,6] => [4,2,2,1,1]
[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] => [1,2,3,10,4,9,8,7,6,5] => [4,2,1,1,1,1]
[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] => [1,2,3,10,9,8,7,6,5,4] => [4,1,1,1,1,1,1]
[3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => [1,2,10,3,4,9,5,6,8,7] => [3,3,3,1]
[3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => [1,2,10,3,4,9,5,8,6,7] => [3,3,2,2]
[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] => [1,2,10,3,4,9,5,8,7,6] => [3,3,2,1,1]
[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] => [1,2,10,3,4,9,8,7,6,5] => [3,3,1,1,1,1]
[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] => [1,2,10,3,9,4,8,5,7,6] => [3,2,2,2,1]
[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] => [1,2,10,3,9,4,8,7,6,5] => [3,2,2,1,1,1]
[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] => [1,2,10,3,9,8,7,6,5,4] => [3,2,1,1,1,1,1]
[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] => [1,2,10,9,8,7,6,5,4,3] => [3,1,1,1,1,1,1,1]
[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] => [1,10,2,9,3,8,4,7,5,6] => [2,2,2,2,2]
[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] => [1,10,2,9,3,8,4,7,6,5] => [2,2,2,2,1,1]
[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] => [1,10,2,9,3,8,7,6,5,4] => [2,2,2,1,1,1,1]
[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] => [1,10,2,9,8,7,6,5,4,3] => [2,2,1,1,1,1,1,1]
[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] => [1,10,9,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1,1,1]
[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] => [1,1,1,1,1,1,1,1,1,1]
[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] => [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] => [1,2,3,4,5,12,6,7,8,9,10,11] => [6,6]
[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] => [1,2,3,4,5,12,6,7,8,11,9,10] => [6,4,2]
[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] => [1,2,3,12,4,5,6,11,7,10,8,9] => [4,4,2,2]
[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] => [1,2,3,12,4,11,5,10,6,9,7,8] => [4,2,2,2,2]
[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] => [1,12,2,11,3,10,4,9,5,8,6,7] => [2,2,2,2,2,2]
[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] => [1,1,1,1,1,1,1,1,1,1,1,1]
[] => [] => [] => [] => []
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
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.