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] => [1,2,3] => [1,2,3] => 0
[2,1,3] => [1,3,2] => [1,2,3] => [1,2,3] => 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] => [1,2,3,4] => [1,2,3,4] => 0
[1,3,2,4] => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,3,4,2] => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
[1,4,2,3] => [1,4,2,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,4,3,2] => [1,4,2,3] => [1,2,4,3] => [1,2,4,3] => 1
[2,1,3,4] => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
[2,1,4,3] => [1,4,2,3] => [1,2,4,3] => [1,2,4,3] => 1
[2,3,1,4] => [1,4,2,3] => [1,2,4,3] => [1,2,4,3] => 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] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,3,1] => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[3,1,2,4] => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[3,1,4,2] => [1,4,2,3] => [1,2,4,3] => [1,2,4,3] => 1
[3,2,1,4] => [1,4,2,3] => [1,2,4,3] => [1,2,4,3] => 1
[3,2,4,1] => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 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] => [1,2,3,4] => [1,2,3,4] => 0
[4,2,1,3] => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 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
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 Stasinski-Voll length of a signed permutation.
The Stasinski-Voll length of a signed permutation $\sigma$ is
$$ L(\sigma) = \frac{1}{2} \#\{(i,j) ~\mid -n \leq i < j \leq n,~ i \not\equiv j \operatorname{mod} 2,~ \sigma(i) > \sigma(j)\}, $$
where $n$ is the size of $\sigma$.
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.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.