Identifier
Values
[1,0] => [1] => [1] => [-1] => 0
[1,0,1,0] => [2,1] => [2,1] => [1,-2] => 0
[1,1,0,0] => [1,2] => [1,2] => [-2,1] => 0
[1,0,1,0,1,0] => [3,2,1] => [3,2,1] => [1,2,-3] => 0
[1,0,1,1,0,0] => [2,3,1] => [2,3,1] => [2,1,-3] => 0
[1,1,0,0,1,0] => [3,1,2] => [3,1,2] => [2,-3,1] => 0
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [1,-3,2] => 0
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [-3,1,2] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => [1,2,3,-4] => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [3,4,2,1] => [2,1,3,-4] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [4,2,3,1] => [2,3,1,-4] => 0
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [1,3,2,-4] => 0
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => [3,1,2,-4] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [4,3,1,2] => [2,3,-4,1] => 0
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,4,1,2] => [3,2,-4,1] => 0
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [4,2,1,3] => [1,3,-4,2] => 0
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4] => [1,2,-4,3] => 0
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [2,3,1,4] => [2,1,-4,3] => 0
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,1,2,3] => [3,-4,1,2] => 0
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,1,2,4] => [2,-4,1,3] => 0
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [1,-4,2,3] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [-4,1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,-5] => 0
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [4,3,5,2,1] => [1,3,2,4,-5] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [5,3,2,4,1] => [1,3,4,2,-5] => 0
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [1,2,4,3,-5] => 0
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [1,4,2,3,-5] => 0
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [5,4,2,1,3] => [1,3,4,-5,2] => 0
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [5,3,2,1,4] => [1,2,4,-5,3] => 0
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,3,2,1,5] => [1,2,3,-5,4] => 0
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,2,4,1,5] => [1,3,2,-5,4] => 0
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [5,2,1,3,4] => [1,4,-5,2,3] => 0
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [4,2,1,3,5] => [1,3,-5,2,4] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4,5] => [1,2,-5,3,4] => 0
[1,1,1,1,0,1,0,0,0,0] => [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
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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.