- FindStat

Identifier

Mp00245: Signed permutations —standardize⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Map

standardize

Description

Return the standardization of the signed permutation, where 1 is the smallest and -1 the largest element.
Let $\pi\in\mathfrak H_n$ be a signed permutation. Assuming the order $1 < \dots < n < -n < \dots < -1$, this map returns the permutation in $\mathfrak S_n$ which is order isomorphic to $\pi(1),\dots,\pi(n)$.

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

conjugate

Description

Sends a standard tableau to its conjugate tableau.