Identifier
Values
[1] => [1] => 0
[1,2] => [1,2] => 0
[2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => 2
[2,3,1] => [2,3,1] => 4
[3,1,2] => [3,1,2] => 2
[3,2,1] => [3,2,1] => 2
[1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => 2
[1,3,2,4] => [1,3,2,4] => 2
[1,3,4,2] => [1,3,4,2] => 4
[1,4,2,3] => [1,4,2,3] => 2
[1,4,3,2] => [1,4,3,2] => 2
[2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [2,3,1,4] => 4
[2,3,4,1] => [2,3,4,1] => 6
[2,4,1,3] => [2,4,1,3] => 4
[2,4,3,1] => [2,4,3,1] => 4
[3,1,2,4] => [3,1,2,4] => 2
[3,1,4,2] => [3,1,4,2] => 4
[3,2,1,4] => [3,2,1,4] => 2
[3,2,4,1] => [3,2,4,1] => 4
[3,4,1,2] => [3,4,1,2] => 4
[3,4,2,1] => [3,4,2,1] => 4
[4,1,2,3] => [4,1,2,3] => 2
[4,1,3,2] => [4,1,3,2] => 2
[4,2,1,3] => [4,2,1,3] => 2
[4,2,3,1] => [4,2,3,1] => 2
[4,3,1,2] => [4,3,1,2] => 4
[4,3,2,1] => [4,3,2,1] => 4
[1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,4,5,3] => 4
[1,2,5,3,4] => [1,2,5,3,4] => 2
[1,2,5,4,3] => [1,2,5,4,3] => 2
[1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,3,4,2,5] => 4
[1,3,4,5,2] => [1,3,4,5,2] => 6
[1,3,5,2,4] => [1,3,5,2,4] => 4
[1,3,5,4,2] => [1,3,5,4,2] => 4
[1,4,2,3,5] => [1,4,2,3,5] => 2
[1,4,2,5,3] => [1,4,2,5,3] => 4
[1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,3,5,2] => [1,4,3,5,2] => 4
[1,4,5,2,3] => [1,4,5,2,3] => 4
[1,4,5,3,2] => [1,4,5,3,2] => 4
[1,5,2,3,4] => [1,5,2,3,4] => 2
[1,5,2,4,3] => [1,5,2,4,3] => 2
[1,5,3,2,4] => [1,5,3,2,4] => 2
[1,5,3,4,2] => [1,5,3,4,2] => 2
[1,5,4,2,3] => [1,5,4,2,3] => 4
[1,5,4,3,2] => [1,5,4,3,2] => 4
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 excedance statistic of a signed permutation.
This is the number of negative entries plus twice the number of excedances of the signed permutation. That is,
$$fexc(\sigma) = 2exc(\sigma) + neg(\sigma),$$
where
$$exc(\sigma) = |\{i \in [n-1] \,:\, \sigma(i) > i\}|$$
$$neg(\sigma) = |\{i \in [n] \,:\, \sigma(i) < 0\}|$$
It has the same distribution as the flag descent statistic.
Map
to signed permutation
Description
The signed permutation with all signs positive.