Identifier
Values
[1,0] => [2,1] => 1
[1,0,1,0] => [3,1,2] => 1
[1,1,0,0] => [2,3,1] => 2
[1,0,1,0,1,0] => [4,1,2,3] => 1
[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] => 1
[1,1,1,0,0,0] => [2,3,4,1] => 3
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[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] => 2
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 3
[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] => 3
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 1
[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] => 3
[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] => 1
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 1
[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] => 2
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 2
[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] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 2
[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] => 2
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 1
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 4
[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] => 3
[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] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 4
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 1
[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] => 1
[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] => 2
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => 1
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => 1
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 3
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 3
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 4
[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] => 3
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => 1
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 2
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 4
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => 3
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => 2
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => 1
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[] => [1] => 1
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Description
The number of left-to-right-maxima of a permutation.
An integer $\sigma_i$ in the one-line notation of a permutation $\sigma$ is a left-to-right-maximum if there does not exist a $j < i$ such that $\sigma_j > \sigma_i$.
This is also the number of weak exceedences of a permutation that are not mid-points of a decreasing subsequence of length 3, see [1] for more on the later description.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.