Identifier
Values
[1] => [1] => [1] => [1] => 0
[1,1] => [1,2] => [2,1] => [2,1] => 0
[1,2] => [1,2] => [2,1] => [2,1] => 0
[2,1] => [2,1] => [1,2] => [1,2] => 0
[1,1,1] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,1,2] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,2,1] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[2,1,1] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[1,1,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,3,1] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[3,1,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,2,2] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[2,1,2] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,2,1] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[2,1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,3,1] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[3,1,2] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [3,2,1] => [2,1,3] => [2,1,3] => 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 edges in the reduced word graph of a signed permutation.
The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
Map
to car permutation
Description
Maps a parking function to the permutation of cars that correspond to that parking function.
For example, the image $[2, 4, 5, 6, 3, 1, 7]$ means that car 2 takes spots 1, car 4 takes spot 2, and so on.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.