Identifier
Values
[2] => [[1,2]] => [[1,2]] => [[2,0],[1]] => 2
[1,1] => [[1],[2]] => [[1,2]] => [[2,0],[1]] => 2
[3] => [[1,2,3]] => [[1,2,3]] => [[3,0,0],[2,0],[1]] => 3
[2,1] => [[1,3],[2]] => [[1,2],[3]] => [[2,1,0],[2,0],[1]] => 2
[1,1,1] => [[1],[2],[3]] => [[1,2],[3]] => [[2,1,0],[2,0],[1]] => 2
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 difference of the first and last value in the first row of the 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
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.