FullSupportReflectionCount on CartanType
The reflections whose reduced words use every simple reflection: n h / |W| times the product of the codegrees d - 2 (leaving out the degree 2).
Called as CombinatorialStat(x, "FullSupportReflectionCount"). 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 St000855
The number of full-support reflections in the Weyl group 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/St000855 has the rest.