AscentCountIncludingLargestEntry on StandardTableau
Entries whose successor is in the same or a higher row, and the largest entry.
The size less the descents of the tableau; FindStat's St000507 counts the largest entry, which has no successor, as an ascent. The empty tableau gives 0.
Called as CombinatorialStat(x, "AscentCountIncludingLargestEntry"). The head's page has its examples.
Live
Distribution
Over StandardTableaux at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000507
The number of ascents of a standard tableau.
| Object | Value |
|---|---|
[] | 0 |
[[1]] | 1 |
[[1,2]] | 2 |
[[1,2,3]] | 3 |
[[1],[2]] | 1 |
[[1,2,3,4]] | 4 |
[[1,2],[3]] | 2 |
[[1,3],[2]] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000507 has the rest.