StandardImmaculateTableauCount on IntegerComposition
Standard immaculate tableaux of the shape: fillings of 1 .. n increasing along the rows and down the first column.
Berg, Bergeron, Saliola, Serrano and Zabrocki, A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions (Proposition 3.13).
Called as CombinatorialStat(x, "StandardImmaculateTableauCount"). 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 St000047
The number of standard immaculate tableaux of a given shape.
| 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/St000047 has the rest.