Identifier
Values
[1,0] => [1,0] => [1] => [1] => 0
[1,0,1,0] => [1,1,0,0] => [2,1] => [2,1] => 0
[1,1,0,0] => [1,0,1,0] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [3,1,2] => [3,1,2] => 0
[1,0,1,1,0,0] => [1,0,1,1,0,0] => [1,3,2] => [1,3,2] => 0
[1,1,0,0,1,0] => [1,1,0,1,0,0] => [2,3,1] => [2,3,1] => 0
[1,1,0,1,0,0] => [1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 1
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => [4,1,2,3] => 0
[1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,4,2,3] => 0
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [2,4,1,3] => [2,4,1,3] => 0
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => [3,1,2,4] => [3,1,2,4] => 2
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => 0
[1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => [3,4,1,2] => 0
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,3,4,2] => 0
[1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => [3,1,4,2] => 1
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => 1
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => 1
[1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => 0
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => 2
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,4,2,3,5] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => 0
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,4,5,3] => 0
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,3,4,5,2] => 0
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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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 signed permutation
Description
The signed permutation with all signs positive.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.