- FindStat

Identifier

Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 4359 entries. <<<

Map

reverse

Description

The reversal of a signed permutation.

Map

permutation

Description

The permutation obtained by forgetting the colours.

Map

to increasing tree

Description

Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.