Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
St000102: Semistandard tableaux ⟶ ℤ
Values
{{1}} => [1] => [[1]] => [[1]] => 0
{{1,2}} => [2,1] => [[0,1],[1,0]] => [[1,2],[2]] => 0
{{1},{2}} => [1,2] => [[1,0],[0,1]] => [[1,1],[2]] => 0
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Description
The charge of a semistandard tableau.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
to alternating sign matrix
Description
Maps a permutation to its permutation matrix as an alternating sign matrix.
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.
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.
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