Identifier
Values
[1] => [[1]] => [[1]] => [1] => 0
[1,2] => [[1,0],[0,1]] => [[1,1],[2]] => [3,1,2] => 2
[2,1] => [[0,1],[1,0]] => [[1,2],[2]] => [2,1,3] => 1
[1,2,3] => [[1,0,0],[0,1,0],[0,0,1]] => [[1,1,1],[2,2],[3]] => [6,4,5,1,2,3] => 11
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]] => [[1,1,1],[2,3],[3]] => [5,4,6,1,2,3] => 10
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]] => [[1,1,2],[2,2],[3]] => [6,3,4,1,2,5] => 10
[2,3,1] => [[0,0,1],[1,0,0],[0,1,0]] => [[1,1,3],[2,3],[3]] => [4,3,5,1,2,6] => 8
[3,1,2] => [[0,1,0],[0,0,1],[1,0,0]] => [[1,2,2],[2,3],[3]] => [5,2,6,1,3,4] => 8
[3,2,1] => [[0,0,1],[0,1,0],[1,0,0]] => [[1,2,3],[2,3],[3]] => [4,2,5,1,3,6] => 7
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Description
The load of a permutation.
The definition of the load of a finite word in a totally ordered alphabet can be found in [1], for permutations, it is given by the major index St000004The major index of a permutation. of the reverse Mp00064reverse of the inverse Mp00066inverse permutation.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
Map
to semistandard tableau via monotone triangles
Description
The semistandard tableau corresponding the monotone triangle of an alternating sign matrix.
This is obtained by interpreting each row of the monotone triangle as an integer partition, and filling the cells of the smallest partition with ones, the second smallest with twos, and so on.
Map
to alternating sign matrix
Description
Maps a permutation to its permutation matrix as an alternating sign matrix.