CoxeterElementFactorizationCount on CartanType
The ways to write a Coxeter element as a product of n reflections: n! h^n / |W|.
Called as CombinatorialStat(x, "CoxeterElementFactorizationCount"). 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 St000858
The number of factorizations of any Coxeter element into reflections of a finite Cartan type.
| Object | Value |
|---|---|
['A',1] | 1 |
['A',2] | 3 |
['A',3] | 16 |
['A',4] | 125 |
['A',5] | 1296 |
['A',6] | 16807 |
['A',7] | 262144 |
['A',8] | 4782969 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000858 has the rest.