Identifier
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
[1] => [[1]] => [1] => [1]
[2] => [[1,2]] => [1,2] => [2]
[1,1] => [[1],[2]] => [2,1] => [1,1]
[3] => [[1,2,3]] => [1,2,3] => [3]
[2,1] => [[1,3],[2]] => [2,1,3] => [1,2]
[1,1,1] => [[1],[2],[3]] => [3,2,1] => [1,1,1]
[4] => [[1,2,3,4]] => [1,2,3,4] => [4]
[3,1] => [[1,3,4],[2]] => [2,1,3,4] => [1,3]
[2,2] => [[1,2],[3,4]] => [3,4,1,2] => [2,2]
[2,1,1] => [[1,4],[2],[3]] => [3,2,1,4] => [1,1,2]
[1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => [1,1,1,1]
[5] => [[1,2,3,4,5]] => [1,2,3,4,5] => [5]
[4,1] => [[1,3,4,5],[2]] => [2,1,3,4,5] => [1,4]
[3,2] => [[1,2,5],[3,4]] => [3,4,1,2,5] => [2,3]
[3,1,1] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => [1,1,3]
[2,2,1] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => [1,2,2]
[2,1,1,1] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => [1,1,1,2]
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [1,1,1,1,1]
[6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [6]
[5,1] => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [1,5]
[4,2] => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [2,4]
[4,1,1] => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [1,1,4]
[3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [3,3]
[3,2,1] => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
[3,1,1,1] => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [1,1,1,3]
[2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [2,2,2]
[2,2,1,1] => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
[2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [1,1,1,1,2]
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [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] => [7]
[6,1] => [[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => [1,6]
[5,2] => [[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => [2,5]
[5,1,1] => [[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [1,1,5]
[4,3] => [[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => [3,4]
[4,2,1] => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
[4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [1,1,1,4]
[3,3,1] => [[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [1,3,3]
[3,2,2] => [[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [2,2,3]
[3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
[3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [1,1,1,1,3]
[2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
[2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
[2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [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] => [8]
[7,1] => [[1,3,4,5,6,7,8],[2]] => [2,1,3,4,5,6,7,8] => [1,7]
[6,2] => [[1,2,5,6,7,8],[3,4]] => [3,4,1,2,5,6,7,8] => [2,6]
[6,1,1] => [[1,4,5,6,7,8],[2],[3]] => [3,2,1,4,5,6,7,8] => [1,1,6]
[5,3] => [[1,2,3,7,8],[4,5,6]] => [4,5,6,1,2,3,7,8] => [3,5]
[5,2,1] => [[1,3,6,7,8],[2,5],[4]] => [4,2,5,1,3,6,7,8] => [1,2,5]
[5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => [4,3,2,1,5,6,7,8] => [1,1,1,5]
[4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [4,4]
[4,3,1] => [[1,3,4,8],[2,6,7],[5]] => [5,2,6,7,1,3,4,8] => [1,3,4]
[4,2,2] => [[1,2,7,8],[3,4],[5,6]] => [5,6,3,4,1,2,7,8] => [2,2,4]
[4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8] => [1,1,2,4]
[4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8] => [1,1,1,1,4]
[3,3,2] => [[1,2,5],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5] => [2,3,3]
[3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5] => [1,1,3,3]
[3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
[3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8] => [1,1,1,2,3]
[3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8] => [1,1,1,1,1,3]
[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4] => [1,1,2,2,2]
[2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6] => [1,1,1,1,2,2]
[2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1]
[9] => [[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => [9]
[8,1] => [[1,3,4,5,6,7,8,9],[2]] => [2,1,3,4,5,6,7,8,9] => [1,8]
[7,2] => [[1,2,5,6,7,8,9],[3,4]] => [3,4,1,2,5,6,7,8,9] => [2,7]
[7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => [3,2,1,4,5,6,7,8,9] => [1,1,7]
[6,3] => [[1,2,3,7,8,9],[4,5,6]] => [4,5,6,1,2,3,7,8,9] => [3,6]
[6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => [4,2,5,1,3,6,7,8,9] => [1,2,6]
[6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9] => [1,1,1,6]
[5,4] => [[1,2,3,4,9],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9] => [4,5]
[5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => [5,2,6,7,1,3,4,8,9] => [1,3,5]
[5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9] => [2,2,5]
[5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8,9] => [1,1,2,5]
[5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9] => [1,1,1,1,5]
[4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => [6,2,7,8,9,1,3,4,5] => [1,4,4]
[4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9] => [2,3,4]
[4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5,9] => [1,1,3,4]
[4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8,9] => [1,2,2,4]
[4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8,9] => [1,1,1,2,4]
[4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9] => [1,1,1,1,1,4]
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => [3,3,3]
[3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => [7,4,8,2,5,9,1,3,6] => [1,2,3,3]
[3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => [7,4,3,2,8,9,1,5,6] => [1,1,1,3,3]
[3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9] => [2,2,2,3]
[3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4,9] => [1,1,2,2,3]
[3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6,9] => [1,1,1,1,2,3]
[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] => [1,1,1,1,1,1,3]
[2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3] => [1,2,2,2,2]
[2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => [8,6,4,3,9,2,7,1,5] => [1,1,1,2,2,2]
[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] => [1,1,1,1,1,2,2]
[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] => [1,1,1,1,1,1,1,2]
[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] => [1,1,1,1,1,1,1,1,1]
[10] => [[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => [10]
[9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => [2,1,3,4,5,6,7,8,9,10] => [1,9]
[8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [3,4,1,2,5,6,7,8,9,10] => [2,8]
[8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => [3,2,1,4,5,6,7,8,9,10] => [1,1,8]
[7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => [4,5,6,1,2,3,7,8,9,10] => [3,7]
>>> Load all 192 entries. <<<
[7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => [4,2,5,1,3,6,7,8,9,10] => [1,2,7]
[7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9,10] => [1,1,1,7]
[6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9,10] => [4,6]
[6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => [5,2,6,7,1,3,4,8,9,10] => [1,3,6]
[6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9,10] => [2,2,6]
[6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8,9,10] => [1,1,2,6]
[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] => [1,1,1,1,6]
[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [5,5]
[5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => [6,2,7,8,9,1,3,4,5,10] => [1,4,5]
[5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9,10] => [2,3,5]
[5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5,9,10] => [1,1,3,5]
[5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8,9,10] => [1,2,2,5]
[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] => [1,1,1,2,5]
[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] => [1,1,1,1,1,5]
[4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => [7,8,3,4,9,10,1,2,5,6] => [2,4,4]
[4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => [7,3,2,8,9,10,1,4,5,6] => [1,1,4,4]
[4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3,10] => [3,3,4]
[4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => [7,4,8,2,5,9,1,3,6,10] => [1,2,3,4]
[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] => [1,1,1,3,4]
[4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9,10] => [2,2,2,4]
[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] => [1,1,2,2,4]
[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] => [1,1,1,1,2,4]
[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] => [1,1,1,1,1,1,4]
[3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => [8,5,9,10,2,6,7,1,3,4] => [1,3,3,3]
[3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => [8,9,5,6,3,4,10,1,2,7] => [2,2,3,3]
[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] => [1,1,2,3,3]
[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] => [1,1,1,1,3,3]
[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] => [1,2,2,2,3]
[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] => [1,1,1,2,2,3]
[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] => [1,1,1,1,1,2,3]
[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] => [1,1,1,1,1,1,1,3]
[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] => [2,2,2,2,2]
[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] => [1,1,2,2,2,2]
[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] => [1,1,1,1,2,2,2]
[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] => [1,1,1,1,1,1,2,2]
[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] => [1,1,1,1,1,1,1,1,2]
[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] => [1,1,1,1,1,1,1,1,1,1]
[5,4,2] => [[1,2,5,6,11],[3,4,9,10],[7,8]] => [7,8,3,4,9,10,1,2,5,6,11] => [2,4,5]
[5,4,1,1] => [[1,4,5,6,11],[2,8,9,10],[3],[7]] => [7,3,2,8,9,10,1,4,5,6,11] => [1,1,4,5]
[5,3,3] => [[1,2,3,10,11],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3,10,11] => [3,3,5]
[5,3,2,1] => [[1,3,6,10,11],[2,5,9],[4,8],[7]] => [7,4,8,2,5,9,1,3,6,10,11] => [1,2,3,5]
[5,3,1,1,1] => [[1,5,6,10,11],[2,8,9],[3],[4],[7]] => [7,4,3,2,8,9,1,5,6,10,11] => [1,1,1,3,5]
[5,2,2,2] => [[1,2,9,10,11],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9,10,11] => [2,2,2,5]
[5,2,2,1,1] => [[1,4,9,10,11],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4,9,10,11] => [1,1,2,2,5]
[4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => [8,9,10,4,5,6,11,1,2,3,7] => [3,4,4]
[4,4,2,1] => [[1,3,6,7],[2,5,10,11],[4,9],[8]] => [8,4,9,2,5,10,11,1,3,6,7] => [1,2,4,4]
[4,4,1,1,1] => [[1,5,6,7],[2,9,10,11],[3],[4],[8]] => [8,4,3,2,9,10,11,1,5,6,7] => [1,1,1,4,4]
[4,3,3,1] => [[1,3,4,11],[2,6,7],[5,9,10],[8]] => [8,5,9,10,2,6,7,1,3,4,11] => [1,3,3,4]
[4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => [8,9,5,6,3,4,10,1,2,7,11] => [2,2,3,4]
[4,3,2,1,1] => [[1,4,7,11],[2,6,10],[3,9],[5],[8]] => [8,5,3,9,2,6,10,1,4,7,11] => [1,1,2,3,4]
[4,2,2,2,1] => [[1,3,10,11],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3,10,11] => [1,2,2,2,4]
[3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => [9,10,6,7,11,3,4,8,1,2,5] => [2,3,3,3]
[3,3,3,1,1] => [[1,4,5],[2,7,8],[3,10,11],[6],[9]] => [9,6,3,10,11,2,7,8,1,4,5] => [1,1,3,3,3]
[3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => [9,6,10,4,7,2,5,11,1,3,8] => [1,2,2,3,3]
[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] => [6,6]
[6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => [7,8,3,4,9,10,1,2,5,6,11,12] => [2,4,6]
[5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => [8,9,10,4,5,6,11,1,2,3,7,12] => [3,4,5]
[5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => [8,4,9,2,5,10,11,1,3,6,7,12] => [1,2,4,5]
[5,4,1,1,1] => [[1,5,6,7,12],[2,9,10,11],[3],[4],[8]] => [8,4,3,2,9,10,11,1,5,6,7,12] => [1,1,1,4,5]
[5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => [8,5,9,10,2,6,7,1,3,4,11,12] => [1,3,3,5]
[5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => [8,9,5,6,3,4,10,1,2,7,11,12] => [2,2,3,5]
[5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => [8,5,3,9,2,6,10,1,4,7,11,12] => [1,1,2,3,5]
[5,2,2,2,1] => [[1,3,10,11,12],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3,10,11,12] => [1,2,2,2,5]
[4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => [9,5,10,11,2,6,7,12,1,3,4,8] => [1,3,4,4]
[4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => [9,10,5,6,3,4,11,12,1,2,7,8] => [2,2,4,4]
[4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => [9,5,3,10,2,6,11,12,1,4,7,8] => [1,1,2,4,4]
[4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => [9,10,6,7,11,3,4,8,1,2,5,12] => [2,3,3,4]
[4,3,3,1,1] => [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]] => [9,6,3,10,11,2,7,8,1,4,5,12] => [1,1,3,3,4]
[4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => [9,6,10,4,7,2,5,11,1,3,8,12] => [1,2,2,3,4]
[3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => [10,7,11,4,8,12,2,5,9,1,3,6] => [1,2,3,3,3]
[3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => [10,7,5,11,3,8,2,6,12,1,4,9] => [1,1,2,2,3,3]
[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] => [2,2,2,2,2,2]
[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] => [1,1,1,1,1,1,1,1,1,1,1,1]
[5,4,3,1] => [[1,3,4,8,13],[2,6,7,12],[5,10,11],[9]] => [9,5,10,11,2,6,7,12,1,3,4,8,13] => [1,3,4,5]
[5,4,2,2] => [[1,2,7,8,13],[3,4,11,12],[5,6],[9,10]] => [9,10,5,6,3,4,11,12,1,2,7,8,13] => [2,2,4,5]
[5,4,2,1,1] => [[1,4,7,8,13],[2,6,11,12],[3,10],[5],[9]] => [9,5,3,10,2,6,11,12,1,4,7,8,13] => [1,1,2,4,5]
[5,3,3,2] => [[1,2,5,12,13],[3,4,8],[6,7,11],[9,10]] => [9,10,6,7,11,3,4,8,1,2,5,12,13] => [2,3,3,5]
[5,3,3,1,1] => [[1,4,5,12,13],[2,7,8],[3,10,11],[6],[9]] => [9,6,3,10,11,2,7,8,1,4,5,12,13] => [1,1,3,3,5]
[5,3,2,2,1] => [[1,3,8,12,13],[2,5,11],[4,7],[6,10],[9]] => [9,6,10,4,7,2,5,11,1,3,8,12,13] => [1,2,2,3,5]
[4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => [10,11,6,7,12,3,4,8,13,1,2,5,9] => [2,3,4,4]
[4,4,3,1,1] => [[1,4,5,9],[2,7,8,13],[3,11,12],[6],[10]] => [10,6,3,11,12,2,7,8,13,1,4,5,9] => [1,1,3,4,4]
[4,4,2,2,1] => [[1,3,8,9],[2,5,12,13],[4,7],[6,11],[10]] => [10,6,11,4,7,2,5,12,13,1,3,8,9] => [1,2,2,4,4]
[4,3,3,2,1] => [[1,3,6,13],[2,5,9],[4,8,12],[7,11],[10]] => [10,7,11,4,8,12,2,5,9,1,3,6,13] => [1,2,3,3,4]
[5,4,3,2] => [[1,2,5,9,14],[3,4,8,13],[6,7,12],[10,11]] => [10,11,6,7,12,3,4,8,13,1,2,5,9,14] => [2,3,4,5]
[5,4,3,1,1] => [[1,4,5,9,14],[2,7,8,13],[3,11,12],[6],[10]] => [10,6,3,11,12,2,7,8,13,1,4,5,9,14] => [1,1,3,4,5]
[5,4,2,2,1] => [[1,3,8,9,14],[2,5,12,13],[4,7],[6,11],[10]] => [10,6,11,4,7,2,5,12,13,1,3,8,9,14] => [1,2,2,4,5]
[5,3,3,2,1] => [[1,3,6,13,14],[2,5,9],[4,8,12],[7,11],[10]] => [10,7,11,4,8,12,2,5,9,1,3,6,13,14] => [1,2,3,3,5]
[4,4,3,2,1] => [[1,3,6,10],[2,5,9,14],[4,8,13],[7,12],[11]] => [11,7,12,4,8,13,2,5,9,14,1,3,6,10] => [1,2,3,4,4]
[5,4,3,2,1] => [[1,3,6,10,15],[2,5,9,14],[4,8,13],[7,12],[11]] => [11,7,12,4,8,13,2,5,9,14,1,3,6,10,15] => [1,2,3,4,5]
[] => [] => [] => []
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
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.