Identifier
Values
[(1,2)] => [2,1] => [1,2] => [[1,0],[0,1]] => 1
[(1,2),(3,4)] => [2,1,4,3] => [3,2,1,4] => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]] => 1
[(1,3),(2,4)] => [3,4,1,2] => [4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]] => 1
[(1,4),(2,3)] => [4,3,2,1] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => 1
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => [[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 1
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,5,2,3,1,6] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 1
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [5,4,3,2,1,6] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 1
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [1,5,4,2,3,6] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 1
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [3,2,1,4,5,6] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 1
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [4,1,3,2,5,6] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 1
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [5,1,2,4,3,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 1
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 1
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 permanent of an alternating sign matrix.
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
Map
to alternating sign matrix
Description
Maps a permutation to its permutation matrix as an alternating sign matrix.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.