- FindStat

Identifier

Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions

Images

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

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

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

[1,0,1,0,1,0] => [3,2,1] => [1,1,1]

[1,0,1,1,0,0] => [2,3,1] => [2,1]

[1,1,0,0,1,0] => [3,1,2] => [2,1]

[1,1,0,1,0,0] => [2,1,3] => [2,1]

[1,1,1,0,0,0] => [1,2,3] => [3]

[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,1,1,1]

[1,0,1,0,1,1,0,0] => [3,4,2,1] => [2,1,1]

[1,0,1,1,0,0,1,0] => [4,2,3,1] => [2,1,1]

[1,0,1,1,0,1,0,0] => [3,2,4,1] => [2,1,1]

[1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,1]

[1,1,0,0,1,0,1,0] => [4,3,1,2] => [2,1,1]

[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,2]

[1,1,0,1,0,0,1,0] => [4,2,1,3] => [2,1,1]

[1,1,0,1,0,1,0,0] => [3,2,1,4] => [2,1,1]

[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,1]

[1,1,1,0,0,0,1,0] => [4,1,2,3] => [3,1]

[1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,1]

[1,1,1,0,1,0,0,0] => [2,1,3,4] => [3,1]

[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4]

[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,1,1,1,1]

[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [2,1,1,1]

[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [2,1,1,1]

[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [2,1,1,1]

[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,1,1]

[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [2,1,1,1]

[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [2,2,1]

[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [2,1,1,1]

[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [2,1,1,1]

[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,1,1]

[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [3,1,1]

[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1]

[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,1,1]

[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [4,1]

[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [2,1,1,1]

[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [2,2,1]

[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [2,2,1]

[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [2,2,1]

[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,2]

[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [2,1,1,1]

[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [2,2,1]

[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [2,1,1,1]

[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [2,1,1,1]

[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,1,1]

[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [3,1,1]

[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [3,1,1]

[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,1,1]

[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [4,1]

[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [3,1,1]

[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [3,2]

[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [3,1,1]

[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [3,1,1]

[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [3,2]

[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [3,1,1]

[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [3,1,1]

[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,1,1]

[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [4,1]

[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [4,1]

[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [4,1]

[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [4,1]

[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [4,1]

[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5]

[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,1,1,1,1,1]

[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [2,1,1,1,1]

[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [2,1,1,1,1]

[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [2,1,1,1,1]

[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [3,1,1,1]

[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [2,1,1,1,1]

[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [2,2,1,1]

[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [2,1,1,1,1]

[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [2,1,1,1,1]

[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [3,1,1,1]

[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [3,1,1,1]

[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [3,1,1,1]

[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [3,1,1,1]

[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [4,1,1]

[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [2,1,1,1,1]

[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [2,2,1,1]

[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [2,2,1,1]

[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [2,2,1,1]

[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [3,2,1]

[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [2,1,1,1,1]

[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [2,2,1,1]

[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [2,1,1,1,1]

[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [2,1,1,1,1]

[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [3,1,1,1]

[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [3,1,1,1]

[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [3,1,1,1]

[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [3,1,1,1]

[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,1,1]

[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [3,1,1,1]

[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [3,2,1]

[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [3,1,1,1]

[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [3,1,1,1]

[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,2,1]

[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [3,1,1,1]

[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,1,1,1]

[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [3,1,1,1]

[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [4,1,1]

>>> Load all 1770 entries. <<<

Map

to 132-avoiding permutation

Description

Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].

Map

Robinson-Schensted tableau shape

Description

Sends a permutation to its Robinson-Schensted tableau shape.
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 the shape of its corresponding insertion and recording tableau.