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Identifier
Values
{{1}} => [1] => [[1]] => [[1]] => 1
{{1,2}} => [2,1] => [[0,1],[1,0]] => [[1,2],[2]] => 2
{{1},{2}} => [1,2] => [[1,0],[0,1]] => [[1,1],[2]] => 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 last entry in the first row 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.