Identifier
Values
{{1,2}} => [[1,2]] => [[2,0],[1]] => 2
{{1},{2}} => [[1],[2]] => [[1,1],[1]] => 3
{{1,2,3}} => [[1,2,3]] => [[3,0,0],[2,0],[1]] => 3
{{1,2},{3}} => [[1,2],[3]] => [[2,1,0],[2,0],[1]] => 4
{{1,3},{2}} => [[1,3],[2]] => [[2,1,0],[1,1],[1]] => 5
{{1},{2,3}} => [[1,3],[2]] => [[2,1,0],[1,1],[1]] => 5
{{1},{2},{3}} => [[1],[2],[3]] => [[1,1,1],[1,1],[1]] => 6
{{1,2,3,4}} => [[1,2,3,4]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => 4
{{1,2,3},{4}} => [[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 5
{{1,2,4},{3}} => [[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => 6
{{1,2},{3,4}} => [[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => 6
{{1,2},{3},{4}} => [[1,2],[3],[4]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => 7
{{1,3,4},{2}} => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
{{1,3},{2,4}} => [[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 7
{{1,3},{2},{4}} => [[1,3],[2],[4]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => 8
{{1,4},{2,3}} => [[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 7
{{1},{2,3,4}} => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
{{1},{2,3},{4}} => [[1,3],[2],[4]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => 8
{{1,4},{2},{3}} => [[1,4],[2],[3]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => 9
{{1},{2,4},{3}} => [[1,4],[2],[3]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => 9
{{1},{2},{3,4}} => [[1,4],[2],[3]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => 9
{{1},{2},{3},{4}} => [[1],[2],[3],[4]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => 10
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Description
The number of nonzero entries in a Gelfand Tsetlin pattern.
Map
to Gelfand-Tsetlin pattern
Description
Sends a tableau to its corresponding Gelfand-Tsetlin pattern.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.
Map
Standard tableau associated to a set partition
Description
Sends a set partition to the associated standard tableau.
The $j$th column of the standard tableau associated to a set partition is the set of $j$th smallest elements of its blocks arranged in increassing order.