Identifier
Values
[.,.] => [1] => [1] => [-1] => 0
[.,[.,.]] => [2,1] => [2,1] => [1,-2] => 0
[[.,.],.] => [1,2] => [1,2] => [-2,1] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => [1,2,-3] => 0
[.,[[.,.],.]] => [2,3,1] => [2,3,1] => [2,1,-3] => 0
[[.,.],[.,.]] => [3,1,2] => [3,1,2] => [2,-3,1] => 0
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [1,-3,2] => 0
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [-3,1,2] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => [1,2,3,-4] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,4,2,1] => [2,1,3,-4] => 1
[.,[[.,.],[.,.]]] => [4,2,3,1] => [4,2,3,1] => [2,3,1,-4] => 0
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,4,1] => [1,3,2,-4] => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,4,1] => [3,1,2,-4] => 0
[[.,.],[.,[.,.]]] => [4,3,1,2] => [4,3,1,2] => [2,3,-4,1] => 0
[[.,.],[[.,.],.]] => [3,4,1,2] => [3,4,1,2] => [3,2,-4,1] => 0
[[.,[.,.]],[.,.]] => [4,2,1,3] => [4,2,1,3] => [1,3,-4,2] => 0
[[[.,.],.],[.,.]] => [4,1,2,3] => [4,1,2,3] => [3,-4,1,2] => 0
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => [1,2,-4,3] => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1,4] => [2,1,-4,3] => 0
[[[.,.],[.,.]],.] => [3,1,2,4] => [3,1,2,4] => [2,-4,1,3] => 0
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [1,-4,2,3] => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [-4,1,2,3] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,-5] => 0
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,5,2,1] => [1,3,2,4,-5] => 1
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [5,3,2,4,1] => [1,3,4,2,-5] => 0
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,5,1] => [1,2,4,3,-5] => 0
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,5,1] => [1,4,2,3,-5] => 0
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [5,4,2,1,3] => [1,3,4,-5,2] => 0
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [5,3,2,1,4] => [1,2,4,-5,3] => 0
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [5,2,1,3,4] => [1,4,-5,2,3] => 0
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => [1,2,3,-5,4] => 0
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1,5] => [1,3,2,-5,4] => 0
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [4,2,1,3,5] => [1,3,-5,2,4] => 0
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => [1,2,-5,3,4] => 0
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => [1,-5,2,3,4] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of alignments of type NE of a signed permutation.
An alignment of type NE of a signed permutation $\pi\in\mathfrak H_n$ is a pair $1 \leq i, j\leq n$ such that $\pi(i) < i < j \leq \pi(j)$.
Map
rowmotion
Description
The rowmotion of a signed permutation with respect to the sorting order.
The sorting order on signed permutations (with respect to the Coxeter element $-n, 1, 2,\dots, n-1$) is defined in [1].
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.