Identifier
Values
[1] => [1,0,1,0] => [3,1,2] => 1
[2] => [1,1,0,0,1,0] => [2,4,1,3] => 1
[1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 1
[3] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 3
[2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 4
[1,1,1] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 3
[4] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 8
[3,1] => [1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 6
[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 6
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 8
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 10
[3,2] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 5
[3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 3
[2,2,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 5
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 10
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 8
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 4
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 6
[3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 10
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 4
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 6
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 8
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 9
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => 14
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 7
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => 7
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 7
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 14
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 9
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 14
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 6
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => 14
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 8
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 6
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 14
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 13
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 9
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 9
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 13
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 20
[] => [] => [1] => 0
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Description
The number of occurrences of the pattern 123 or of the pattern 312 in a permutation.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.