StandardCompositionTableauCount on IntegerComposition
Standard composition tableaux of the shape: fillings of 1 .. n with rows decreasing, the first column increasing, and the triple rule.
Luoto, Mykytiuk and van Willigenburg, An introduction to quasisymmetric Schur functions (Definition 4.2.6).
Called as CombinatorialStat(x, "StandardCompositionTableauCount"). The head's page has its examples.
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Distribution
Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000816
The number of standard composition tableaux of the composition.
| 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/St000816 has the rest.