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Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>1 ['A',2]=>2 ['B',2]=>2 ['G',2]=>2 ['A',3]=>6 ['B',3]=>8 ['C',3]=>8 ['A',4]=>24 ['B',4]=>48 ['C',4]=>48 ['D',4]=>32 ['F',4]=>96 ['A',5]=>120 ['B',5]=>384 ['C',5]=>384 ['D',5]=>240 ['A',6]=>720 ['B',6]=>3840 ['C',6]=>3840 ['D',6]=>2304 ['E',6]=>4320 ['A',7]=>5040 ['B',7]=>46080 ['C',7]=>46080 ['D',7]=>26880 ['E',7]=>161280 ['A',8]=>40320 ['B',8]=>645120
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Description
The number of Coxeter elements in the Weyl group of a finite Cartan type.
This is, the elements that are conjugate to the product of the simple generators in any order, or, equivalently, the elements that admit a primitive $h$-th root of unity as an eigenvalue where $h$ is the Coxeter number.
References
[1] Reiner, V., Ripoll, V., Stump, C. On non-conjugate Coxeter elements in well-generated reflection groups MathSciNet:3623739
Code
def statistic(cartan_type):
    W = ReflectionGroup(cartan_type)
    return len(W.coxeter_elements())
Created
Jun 25, 2017 at 20:14 by Christian Stump
Updated
Jun 26, 2017 at 08:34 by Christian Stump