- FindStat

Identifier

Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words

Images

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

[1,2] => [[1,2]] => [1,2] => 0

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

[1,2,3] => [[1,2,3]] => [1,2,3] => 00

[1,3,2] => [[1,2],[3]] => [3,1,2] => 10

[2,1,3] => [[1,3],[2]] => [2,1,3] => 10

[2,3,1] => [[1,3],[2]] => [2,1,3] => 10

[3,1,2] => [[1,2],[3]] => [3,1,2] => 10

[3,2,1] => [[1],[2],[3]] => [3,2,1] => 11

[1,2,3,4] => [[1,2,3,4]] => [1,2,3,4] => 000

[1,2,4,3] => [[1,2,3],[4]] => [4,1,2,3] => 100

[1,3,2,4] => [[1,2,4],[3]] => [3,1,2,4] => 100

[1,3,4,2] => [[1,2,4],[3]] => [3,1,2,4] => 100

[1,4,2,3] => [[1,2,3],[4]] => [4,1,2,3] => 100

[1,4,3,2] => [[1,2],[3],[4]] => [4,3,1,2] => 110

[2,1,3,4] => [[1,3,4],[2]] => [2,1,3,4] => 100

[2,1,4,3] => [[1,3],[2,4]] => [2,4,1,3] => 010

[2,3,1,4] => [[1,3,4],[2]] => [2,1,3,4] => 100

[2,3,4,1] => [[1,3,4],[2]] => [2,1,3,4] => 100

[2,4,1,3] => [[1,3],[2,4]] => [2,4,1,3] => 010

[2,4,3,1] => [[1,3],[2],[4]] => [4,2,1,3] => 110

[3,1,2,4] => [[1,2,4],[3]] => [3,1,2,4] => 100

[3,1,4,2] => [[1,2],[3,4]] => [3,4,1,2] => 010

[3,2,1,4] => [[1,4],[2],[3]] => [3,2,1,4] => 110

[3,2,4,1] => [[1,4],[2],[3]] => [3,2,1,4] => 110

[3,4,1,2] => [[1,2],[3,4]] => [3,4,1,2] => 010

[3,4,2,1] => [[1,4],[2],[3]] => [3,2,1,4] => 110

[4,1,2,3] => [[1,2,3],[4]] => [4,1,2,3] => 100

[4,1,3,2] => [[1,2],[3],[4]] => [4,3,1,2] => 110

[4,2,1,3] => [[1,3],[2],[4]] => [4,2,1,3] => 110

[4,2,3,1] => [[1,3],[2],[4]] => [4,2,1,3] => 110

[4,3,1,2] => [[1,2],[3],[4]] => [4,3,1,2] => 110

[4,3,2,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 111

[1,2,3,4,5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 0000

[1,2,3,5,4] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1000

[1,2,4,3,5] => [[1,2,3,5],[4]] => [4,1,2,3,5] => 1000

[1,2,4,5,3] => [[1,2,3,5],[4]] => [4,1,2,3,5] => 1000

[1,2,5,3,4] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1000

[1,2,5,4,3] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1100

[1,3,2,4,5] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 1000

[1,3,2,5,4] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 0100

[1,3,4,2,5] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 1000

[1,3,4,5,2] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 1000

[1,3,5,2,4] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 0100

[1,3,5,4,2] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1100

[1,4,2,3,5] => [[1,2,3,5],[4]] => [4,1,2,3,5] => 1000

[1,4,2,5,3] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 0100

[1,4,3,2,5] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1100

[1,4,3,5,2] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1100

[1,4,5,2,3] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 0100

[1,4,5,3,2] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => 1100

[1,5,2,3,4] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 1000

[1,5,2,4,3] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1100

[1,5,3,2,4] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1100

[1,5,3,4,2] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => 1100

[1,5,4,2,3] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 1100

[1,5,4,3,2] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1110

[2,1,3,4,5] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1000

[2,1,3,5,4] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0100

[2,1,4,3,5] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0100

[2,1,4,5,3] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0100

[2,1,5,3,4] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0100

[2,1,5,4,3] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 1010

[2,3,1,4,5] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1000

[2,3,1,5,4] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0100

[2,3,4,1,5] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1000

[2,3,4,5,1] => [[1,3,4,5],[2]] => [2,1,3,4,5] => 1000

[2,3,5,1,4] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0100

[2,3,5,4,1] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1100

[2,4,1,3,5] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0100

[2,4,1,5,3] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0100

[2,4,3,1,5] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1100

[2,4,3,5,1] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1100

[2,4,5,1,3] => [[1,3,5],[2,4]] => [2,4,1,3,5] => 0100

[2,4,5,3,1] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => 1100

[2,5,1,3,4] => [[1,3,4],[2,5]] => [2,5,1,3,4] => 0100

[2,5,1,4,3] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 1010

[2,5,3,1,4] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1100

[2,5,3,4,1] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => 1100

[2,5,4,1,3] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => 1010

[2,5,4,3,1] => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => 1110

[3,1,2,4,5] => [[1,2,4,5],[3]] => [3,1,2,4,5] => 1000

[3,1,2,5,4] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 0100

[3,1,4,2,5] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 0100

[3,1,4,5,2] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 0100

[3,1,5,2,4] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 0100

[3,1,5,4,2] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 1010

[3,2,1,4,5] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100

[3,2,1,5,4] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1010

[3,2,4,1,5] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100

[3,2,4,5,1] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100

[3,2,5,1,4] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1010

[3,2,5,4,1] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => 1010

[3,4,1,2,5] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 0100

[3,4,1,5,2] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 0100

[3,4,2,1,5] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100

[3,4,2,5,1] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100

[3,4,5,1,2] => [[1,2,5],[3,4]] => [3,4,1,2,5] => 0100

[3,4,5,2,1] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100

[3,5,1,2,4] => [[1,2,4],[3,5]] => [3,5,1,2,4] => 0100

[3,5,1,4,2] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 1010

>>> Load all 25487 entries. <<<

Map

Robinson-Schensted insertion tableau

Description

Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.

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 word

Description

The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.