Identifier
Values
[1] => [1,0] => [2,1] => 1
[1,1] => [1,0,1,0] => [3,1,2] => 1
[2] => [1,1,0,0] => [2,3,1] => 1
[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => 1
[3] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[1,1,2] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
[1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 2
[1,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
[2,1,1] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 2
[3,1] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 1
[4] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 1
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 2
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 2
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 2
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 2
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 3
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 2
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 2
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 1
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 2
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 2
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 2
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 1
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 2
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 1
[5] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 1
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Description
The number of descents of a permutation.
This can be described as an occurrence of the vincular mesh pattern ([2,1], {(1,0),(1,1),(1,2)}), i.e., the middle column is shaded, see [3].
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.