Identifier
Values
[1] => [1,0] => [2,1] => [2,1] => 0
[2] => [1,0,1,0] => [3,1,2] => [2,3,1] => 0
[1,1] => [1,1,0,0] => [2,3,1] => [3,2,1] => 0
[3] => [1,0,1,0,1,0] => [4,1,2,3] => [2,3,4,1] => 0
[2,1] => [1,0,1,1,0,0] => [3,1,4,2] => [3,4,1,2] => 0
[1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => [2,4,1,3] => 1
[4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => 0
[3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [2,4,5,1,3] => 2
[2,2] => [1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [4,3,5,2,1] => 0
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [2,3,5,1,4] => 1
[5] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 0
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [2,3,5,6,1,4] => 2
[3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [3,5,1,4,2] => 2
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [2,5,4,6,3,1] => 3
[2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [3,2,5,1,4] => 1
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [5,3,4,6,2,1] => 0
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [2,3,4,6,5,1] => 1
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [2,4,6,1,5,3] => 3
[3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [2,5,4,1,3] => 2
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [3,4,1,6,2,5] => 1
[2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => 0
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [3,2,4,6,1,5] => 1
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [4,3,6,5,2,1] => 1
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [2,4,5,6,1,3] => 3
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => 3
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [4,2,3,6,1,5] => 1
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [2,3,6,1,4,5] => 1
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [5,6,4,1,3,2] => 1
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [2,6,4,5,1,3] => 3
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 0
[] => [] => [1] => [1] => 0
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Description
The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.