CoxeterElementCount on CartanType
The Coxeter elements of the Weyl group, one conjugacy class of size |W| / h.
Called as CombinatorialStat(x, "CoxeterElementCount"). 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 St000865
The number of Coxeter elements in the Weyl group of a finite Cartan type.
| Object | Value |
|---|---|
['A',1] | 1 |
['A',2] | 2 |
['A',3] | 6 |
['A',4] | 24 |
['A',5] | 120 |
['A',6] | 720 |
['A',7] | 5040 |
['A',8] | 40320 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000865 has the rest.