PositiveWeylCatalanNumber on CartanType
The positive Catalan number of the type, ∏ (d + h - 2) / d.
Called as CombinatorialStat(x, "PositiveWeylCatalanNumber"). The head's page has its examples.
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Distribution
Over FiniteCartanTypes at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000140
The positive Catalan number of an irreducible finite Cartan type.
| Object | Value |
|---|---|
['A',1] | 1 |
['A',2] | 2 |
['A',3] | 5 |
['A',4] | 14 |
['A',5] | 42 |
['A',6] | 132 |
['A',7] | 429 |
['A',8] | 1430 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000140 has the rest.