Identifier
Values
[1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [3,1,2] => [3,1,2] => 2
[2,1,3] => [2,3,1] => [2,3,1] => 4
[2,3,1] => [2,1,3] => [2,1,3] => 2
[3,1,2] => [1,3,2] => [1,3,2] => 4
[3,2,1] => [3,2,1] => [3,2,1] => 6
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 4
[1,3,4,2] => [3,1,2,4] => [3,1,2,4] => 2
[1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 4
[1,4,3,2] => [4,3,1,2] => [4,3,1,2] => 6
[2,1,3,4] => [2,3,4,1] => [2,3,4,1] => 6
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 8
[2,3,1,4] => [2,3,1,4] => [2,3,1,4] => 4
[2,3,4,1] => [2,1,3,4] => [2,1,3,4] => 2
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => 4
[2,4,3,1] => [4,2,1,3] => [4,2,1,3] => 6
[3,1,2,4] => [1,3,4,2] => [1,3,4,2] => 6
[3,1,4,2] => [3,1,4,2] => [3,1,4,2] => 8
[3,2,1,4] => [3,4,2,1] => [3,4,2,1] => 10
[3,2,4,1] => [3,2,4,1] => [3,2,4,1] => 8
[3,4,1,2] => [3,4,1,2] => [3,4,1,2] => 4
[3,4,2,1] => [3,2,1,4] => [3,2,1,4] => 6
[4,1,2,3] => [1,2,4,3] => [1,2,4,3] => 6
[4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 8
[4,2,1,3] => [2,4,3,1] => [2,4,3,1] => 10
[4,2,3,1] => [4,2,3,1] => [4,2,3,1] => 8
[4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 10
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 12
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 flag major index of a signed permutation.
The flag major index of a signed permutation $\sigma$ is:
$$\operatorname{fmaj}(\sigma)=\operatorname{neg}(\sigma)+2\cdot \sum_{i\in \operatorname{Des}_B(\sigma)}{i} ,$$
where $\operatorname{Des}_B(\sigma)$ is the $B$-descent set of $\sigma$; see [1, Eq.(10)].
This statistic is equidistributed with the $B$-inversions (St001428The number of B-inversions of a signed permutation.) and with the negative major index on the groups of signed permutations (see [1, Corollary 4.6]).
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.