ReflectionCount on CartanType
The number of reflections in the Weyl group, which is the number of positive roots: the sum of the exponents.
Called as CombinatorialStat(x, "ReflectionCount"). 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 St000857
The number of reflections of the Weyl group of a finite Cartan type.
| Object | Value |
|---|---|
['A',1] | 1 |
['A',2] | 3 |
['A',3] | 6 |
['A',4] | 10 |
['A',5] | 15 |
['A',6] | 21 |
['A',7] | 28 |
['A',8] | 36 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000857 has the rest.