NaturalDescentCount on StandardTableau
Entries whose successor is in a strictly higher row.
The opposite of a descent of the tableau (FindStat's St000157), where the successor is in a lower row. An entry whose successor is in its own row is neither.
Called as CombinatorialStat(x, "NaturalDescentCount"). The head's page has its examples.
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Distribution
Over StandardTableaux at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001712
The number of natural descents of a standard Young tableau.
| Object | Value |
|---|---|
[[1]] | 0 |
[[1,2]] | 0 |
[[1,2,3]] | 0 |
[[1],[2]] | 0 |
[[1,2,3,4]] | 0 |
[[1,2],[3]] | 0 |
[[1,3],[2]] | 1 |
[[1,2,3,4,5]] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001712 has the rest.