- FindStat

Identifier

Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 35451 entries. <<<

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.