Identifier
Values
[1] => [1,0] => [2,1] => [2,1] => 0
[1,1] => [1,0,1,0] => [3,1,2] => [3,1,2] => 0
[2] => [1,1,0,0] => [2,3,1] => [2,3,1] => 0
[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => [4,1,2,3] => 0
[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => [3,1,4,2] => 1
[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => [2,4,1,3] => 0
[3] => [1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => 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
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to signed permutation
Description
The signed permutation with all signs positive.