Identifier
Values
[[1,2]] => [[1,2]] => {{1,2}} => [2,1] => 1
[[1],[2]] => [[1,2]] => {{1,2}} => [2,1] => 1
[[1,2,3]] => [[1,2,3]] => {{1,2,3}} => [2,3,1] => 2
[[1,3],[2]] => [[1,2],[3]] => {{1,2},{3}} => [2,1,3] => 1
[[1,2],[3]] => [[1,2,3]] => {{1,2,3}} => [2,3,1] => 2
[[1],[2],[3]] => [[1,2],[3]] => {{1,2},{3}} => [2,1,3] => 1
[[1,2,3,4]] => [[1,2,3,4]] => {{1,2,3,4}} => [2,3,4,1] => 3
[[1,3,4],[2]] => [[1,2,4],[3]] => {{1,2,4},{3}} => [2,4,3,1] => 3
[[1,2,4],[3]] => [[1,2,3],[4]] => {{1,2,3},{4}} => [2,3,1,4] => 2
[[1,2,3],[4]] => [[1,2,3,4]] => {{1,2,3,4}} => [2,3,4,1] => 3
[[1,3],[2,4]] => [[1,2,4],[3]] => {{1,2,4},{3}} => [2,4,3,1] => 3
[[1,2],[3,4]] => [[1,2,3,4]] => {{1,2,3,4}} => [2,3,4,1] => 3
[[1,4],[2],[3]] => [[1,2],[3],[4]] => {{1,2},{3},{4}} => [2,1,3,4] => 1
[[1,3],[2],[4]] => [[1,2,4],[3]] => {{1,2,4},{3}} => [2,4,3,1] => 3
[[1,2],[3],[4]] => [[1,2,3],[4]] => {{1,2,3},{4}} => [2,3,1,4] => 2
[[1],[2],[3],[4]] => [[1,2],[3],[4]] => {{1,2},{3},{4}} => [2,1,3,4] => 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
click to show known generating functions       
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
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
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.