Identifier
Values
[1,0] => [2,1] => [1,2] => [1,2] => 0
[1,0,1,0] => [3,1,2] => [1,3,2] => [1,3,2] => 1
[1,1,0,0] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0] => [4,1,2,3] => [1,4,3,2] => [1,4,3,2] => 2
[1,0,1,1,0,0] => [3,1,4,2] => [1,3,4,2] => [1,3,4,2] => 2
[1,1,0,0,1,0] => [2,4,1,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,1,0,1,0,0] => [4,3,1,2] => [1,4,2,3] => [1,4,2,3] => 2
[1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [1,4,5,3,2] => [1,4,5,3,2] => 3
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,3,5,4,2] => [1,3,5,4,2] => 3
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [1,5,3,4,2] => [1,5,3,4,2] => 4
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,3,4,5,2] => [1,3,4,5,2] => 3
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,2,4,5,3] => [1,2,4,5,3] => 2
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [1,5,4,2,3] => [1,5,4,2,3] => 3
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [1,5,3,2,4] => [1,5,3,2,4] => 3
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [1,4,5,2,3] => [1,4,5,2,3] => 4
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [1,2,5,3,4] => [1,2,5,3,4] => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [1,5,2,3,4] => [1,5,2,3,4] => 3
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[] => [1] => [1] => [1] => 0
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Description
The number of Bruhat lower covers of a permutation.
This is, for a signed permutation $\pi$, the number of signed permutations $\tau$ having a reduced word which is obtained by deleting a letter from a reduced word from $\pi$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.