- FindStat

Identifier

Mp00053: Parking functions —to car permutation⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees

Images

[1] => [1] => [1] => [.,.]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 18248 entries. <<<

Map

to car permutation

Description

Maps a parking function to the permutation of cars that correspond to that parking function.
For example, the image $[2, 4, 5, 6, 3, 1, 7]$ means that car 2 takes spots 1, car 4 takes spot 2, and so on.

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].

Map

binary search tree: left to right

Description

Return the shape of the binary search tree of the permutation as a non labelled binary tree.