Identifier
Values
[1,0] => [2,1] => 1
[1,0,1,0] => [3,1,2] => 2
[1,1,0,0] => [2,3,1] => 1
[1,0,1,0,1,0] => [4,1,2,3] => 2
[1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,0,1,0,0] => [4,3,1,2] => 2
[1,1,1,0,0,0] => [2,3,4,1] => 1
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 2
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 3
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 3
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 2
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 2
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 2
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => 2
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 2
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 3
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 2
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 3
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 3
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 2
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 3
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 3
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => 3
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 3
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 3
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 3
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 3
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 2
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 2
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => 2
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => 2
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => 2
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 3
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => 3
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => 3
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 2
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 2
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 2
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 2
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => 2
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 3
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => 3
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => 2
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 3
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 2
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => 2
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => 3
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => 3
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 1
[] => [1] => 1
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Description
The number of outer peaks of a permutation.
An outer peak in a permutation $w = [w_1,..., w_n]$ is either a position $i$ such that $w_{i-1} < w_i > w_{i+1}$ or $1$ if $w_1 > w_2$ or $n$ if $w_{n} > w_{n-1}$.
In other words, it is a peak in the word $[0,w_1,..., w_n,0]$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.