Identifier
Values
[1] => [1,0,1,0] => [[1,3],[2,4]] => {{1,3},{2,4}} => 2
[2] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => 2
[1,1] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => 1
[2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => 2
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Description
The number of terminal closers of a set partition.
A closer of a set partition is a number that is maximal in its block. In particular, a singleton is a closer. This statistic counts the number of terminal closers. In other words, this is the number of closers such that all larger elements are also closers.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
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.