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
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searching the database for statistics with the same generating function
Description
The permanent of an alternating sign matrix.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
to alternating sign matrix
Description
Maps a permutation to its permutation matrix as 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 $\pi$.