Identifier
Values
{{1}} => [1] => [1] => 0
{{1,2}} => [2,1] => [2,1] => 1
{{1},{2}} => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [2,3,1] => 2
{{1,2},{3}} => [2,1,3] => [2,1,3] => 1
{{1,3},{2}} => [3,2,1] => [3,2,1] => 2
{{1},{2,3}} => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [2,3,4,1] => 3
{{1,2,3},{4}} => [2,3,1,4] => [2,3,1,4] => 2
{{1,2,4},{3}} => [2,4,3,1] => [2,4,3,1] => 3
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}} => [3,2,4,1] => [3,2,4,1] => 3
{{1,3},{2,4}} => [3,4,1,2] => [3,4,1,2] => 4
{{1,3},{2},{4}} => [3,2,1,4] => [3,2,1,4] => 2
{{1,4},{2,3}} => [4,3,2,1] => [4,3,2,1] => 3
{{1},{2,3,4}} => [1,3,4,2] => [1,3,4,2] => 2
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [4,2,3,1] => 4
{{1},{2,4},{3}} => [1,4,3,2] => [1,4,3,2] => 2
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,3,4,5,2] => 3
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,3,4,2,5] => 2
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,3,5,4,2] => 3
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => 2
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,4,3,5,2] => 3
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,4,5,2,3] => 4
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,4,3,2,5] => 2
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,5,4,3,2] => 3
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,4,5,3] => 2
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,5,3,4,2] => 4
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,5,4,3] => 2
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
to signed permutation
Description
The signed permutation with all signs positive.