StandardRibbonTableauCount on IntegerComposition
Standard fillings of the ribbon whose rows have these lengths: the permutations of 1 .. n with these partial sums as their descents.
Stanley, Enumerative Combinatorics, volume 1, section 1.4: Proposition 1.4.1 counts permutations whose descents lie in a set, and inclusion-exclusion over it gives this count. FindStat cites the formula as section 14.4.
Called as CombinatorialStat(x, "StandardRibbonTableauCount"). The head's page has its examples.
Live
Distribution
Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000277
The number of ribbon shaped standard tableaux.
| Object | Value |
|---|---|
[1] | 1 |
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
[8] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000277 has the rest.