ReflectionOrbitCount on CartanType
The conjugacy classes of reflections in the Weyl group: 2 where the simple roots have two lengths (B, C, F, G), else 1.
Called as CombinatorialStat(x, "ReflectionOrbitCount"). The head's page has its examples.
Live
Distribution
Over FiniteCartanTypes at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000854
The number of orbits of reflections of a finite Cartan type.
| Object | Value |
|---|---|
['A',1] | 1 |
['A',2] | 1 |
['A',3] | 1 |
['A',4] | 1 |
['A',5] | 1 |
['A',6] | 1 |
['A',7] | 1 |
['A',8] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000854 has the rest.