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 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.
Map
to signed permutation
Description
The signed permutation with all signs positive.