Identifier
Values
{{1}} => [1] => [1,0,1,0] => [[1,3],[2,4]] => 0
{{1,2}} => [2] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 0
{{1},{2}} => [1,1] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 0
{{1,2,3}} => [3] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 0
{{1,2},{3}} => [2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 0
{{1,3},{2}} => [2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 0
{{1},{2,3}} => [2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 0
{{1},{2},{3}} => [1,1,1] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 0
{{1,2,3},{4}} => [3,1] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 0
{{1,2,4},{3}} => [3,1] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 0
{{1,2},{3,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 0
{{1,2},{3},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 0
{{1,3,4},{2}} => [3,1] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 0
{{1,3},{2,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 0
{{1,3},{2},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 0
{{1,4},{2,3}} => [2,2] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 0
{{1},{2,3,4}} => [3,1] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 0
{{1},{2,3},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 0
{{1,4},{2},{3}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 0
{{1},{2,4},{3}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 0
{{1},{2},{3,4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 0
{{1,2,3},{4,5}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,2,3},{4},{5}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,2,4},{3,5}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,2,4},{3},{5}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,2,5},{3,4}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,2},{3,4,5}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,2},{3,4},{5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,2,5},{3},{4}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,2},{3,5},{4}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,2},{3},{4,5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,3,4},{2,5}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,3,4},{2},{5}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,3,5},{2,4}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,3},{2,4,5}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,3},{2,4},{5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,3,5},{2},{4}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,3},{2,5},{4}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,3},{2},{4,5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,4,5},{2,3}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,4},{2,3,5}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1,4},{2,3},{5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,5},{2,3,4}} => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0
{{1},{2,3,4},{5}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,5},{2,3},{4}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1},{2,3,5},{4}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1},{2,3},{4,5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,4,5},{2},{3}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,4},{2,5},{3}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,4},{2},{3,5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,5},{2,4},{3}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1},{2,4,5},{3}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1},{2,4},{3,5}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1,5},{2},{3,4}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1},{2,5},{3,4}} => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 0
{{1},{2},{3,4,5}} => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 0
{{1,2,3},{4,5},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,3},{4,6},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,3},{4},{5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,4},{3,5},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,4},{3,6},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,4},{3},{5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,5},{3,4},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2},{3,4,5},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,6},{3,4},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2},{3,4,6},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,5},{3,6},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,5},{3},{4,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,6},{3,5},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2},{3,5,6},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2,6},{3},{4,5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,2},{3},{4,5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,4},{2,5},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,4},{2,6},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,4},{2},{5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,5},{2,4},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3},{2,4,5},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,6},{2,4},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3},{2,4,6},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,5},{2,6},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,5},{2},{4,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,6},{2,5},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3},{2,5,6},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3,6},{2},{4,5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,3},{2},{4,5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4,5},{2,3},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4},{2,3,5},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4,6},{2,3},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4},{2,3,6},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,5},{2,3,4},{6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,6},{2,3,4},{5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,3,4},{5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,5,6},{2,3},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,5},{2,3,6},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,6},{2,3,5},{4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,3,5},{4,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,3,6},{4,5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,3},{4,5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4,5},{2,6},{3}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4,5},{2},{3,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4,6},{2,5},{3}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
>>> Load all 116 entries. <<<
{{1,4},{2,5,6},{3}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4,6},{2},{3,5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,4},{2},{3,5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,5,6},{2,4},{3}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,5},{2,4,6},{3}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,6},{2,4,5},{3}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,4,5},{3,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,4,6},{3,5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,4},{3,5,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,5,6},{2},{3,4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,5},{2},{3,4,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,5,6},{3,4}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,5},{3,4,6}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1,6},{2},{3,4,5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
{{1},{2,6},{3,4,5}} => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 0
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 maximal overlap of the cylindrical tableau associated with a tableau.
A cylindrical tableau associated with a standard Young tableau $T$ is the skew row-strict tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle.
The overlap, recorded in this statistic, equals $\max_C\big(2\ell(T) - \ell(C)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.
In particular, the statistic equals $0$, if and only if the last entry of the first row is larger than or equal to the first entry of the last row. Moreover, the statistic attains its maximal value, the number of rows of the tableau minus 1, if and only if the tableau consists of a single column.
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.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.