Identifier
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [-3,1,2] => 0
[2,1,3] => [1,3,2] => [1,3,2] => [-3,1,2] => 0
[2,3,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [-4,1,2,3] => 0
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [-3,1,2,4] => 0
[1,3,4,2] => [1,3,4,2] => [1,3,4,2] => [-4,-3,1,2] => 0
[1,4,2,3] => [1,4,2,3] => [1,4,2,3] => [4,1,2,3] => 1
[1,4,3,2] => [1,4,2,3] => [1,4,2,3] => [4,1,2,3] => 1
[2,1,3,4] => [1,3,4,2] => [1,3,4,2] => [-4,-3,1,2] => 0
[2,1,4,3] => [1,4,2,3] => [1,4,2,3] => [4,1,2,3] => 1
[2,3,1,4] => [1,4,2,3] => [1,4,2,3] => [4,1,2,3] => 1
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [1,3,2,4] => [-3,1,2,4] => 0
[2,4,3,1] => [1,2,4,3] => [1,2,4,3] => [-4,1,2,3] => 0
[3,1,2,4] => [1,2,4,3] => [1,2,4,3] => [-4,1,2,3] => 0
[3,1,4,2] => [1,4,2,3] => [1,4,2,3] => [4,1,2,3] => 1
[3,2,1,4] => [1,4,2,3] => [1,4,2,3] => [4,1,2,3] => 1
[3,2,4,1] => [1,2,4,3] => [1,2,4,3] => [-4,1,2,3] => 0
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [1,3,2,4] => [-3,1,2,4] => 0
[4,2,1,3] => [1,3,2,4] => [1,3,2,4] => [-3,1,2,4] => 0
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,5,2,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[1,5,3,4,2] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[1,5,4,2,3] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[1,5,4,3,2] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[2,1,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[2,1,5,4,3] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[2,3,1,5,4] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[2,3,4,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,1,5,4,2] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[3,2,1,5,4] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[3,4,1,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[3,4,2,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[3,4,5,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,4,5,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,1,5,2,3] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[4,1,5,3,2] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[4,2,1,5,3] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[4,2,3,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[4,3,1,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[4,3,2,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => [1,-5,2,3,4] => 0
[4,5,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,3,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,2,3,4,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,3,4,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,3,4,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,2,1] => [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
Description
The number of excedances of a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) > i\}\rvert$.
Map
Foata-Han inverse
Description
The inverse of the Foata-Han bijection for signed permutations.
This map sends the the flag inversion number St001428The number of B-inversions of a signed permutation. to the flag major index St001433The flag major index of a signed permutation.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
to signed permutation
Description
The signed permutation with all signs positive.