- FindStat

Identifier

Mp00042: Integer partitions —initial 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] => [[1,2],[3]] => [3,1,2] => [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] => [[1,2,3],[4]] => [4,1,2,3] => [1,3]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 193 entries. <<<

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

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

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

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

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

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

[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] => [1,1,1,1,6]

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

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

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

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

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

[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] => [1,1,1,1,1,5]

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

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

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

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

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

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

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

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

[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] => [1,1,1,1,1,1,4]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => [3,3,5]

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

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

[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] => [2,2,2,5]

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

[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] => [3,4,4]

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

[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] => [1,1,1,4,4]

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

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

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

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

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

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

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

[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] => [3,4,5]

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

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

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

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

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

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

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

[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] => [2,2,4,4]

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

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

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

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

[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] => [2,2,2,2,4]

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

[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] => [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] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => [13,10,11,12,6,7,8,9,1,2,3,4,5] => [1,3,4,5]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$ .