- FindStat

Identifier

Mp00226: Standard tableaux —row-to-column-descents⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St000451: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 202 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The length of the longest pattern of the form k 1 2...(k-1).

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

row-to-column-descents

Description

Return a standard tableau whose column descent set equals the row descent set of the original tableau.
A column descent in a standard tableau is an entry $i$ such that $i+1$ appears in a column to the left of the cell containing $i$, in English notation.
A row descent is an entry $i$ such that $i+1$ appears in a row above of the cell containing $i$.

Map

Simion-Schmidt map

Description

The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].