Identifier
Values
[1] => [1,0] => [[1],[2]] => [[1,1],[1]] => 3
[2] => [1,0,1,0] => [[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 7
[1,1] => [1,1,0,0] => [[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => 6
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 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
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.