Identifier
Identifier
Values
['A',1] generating graphics... => 1
['A',2] generating graphics... => 2
['B',2] generating graphics... => 2
['G',2] generating graphics... => 2
['A',3] generating graphics... => 6
['B',3] generating graphics... => 8
['C',3] generating graphics... => 8
['A',4] generating graphics... => 24
['B',4] generating graphics... => 48
['C',4] generating graphics... => 48
['D',4] generating graphics... => 32
['F',4] generating graphics... => 96
['A',5] generating graphics... => 120
['B',5] generating graphics... => 384
['C',5] generating graphics... => 384
['D',5] generating graphics... => 240
['A',6] generating graphics... => 720
['B',6] generating graphics... => 3840
['C',6] generating graphics... => 3840
['D',6] generating graphics... => 2304
['E',6] generating graphics... => 4320
['A',7] generating graphics... => 5040
['B',7] generating graphics... => 46080
['C',7] generating graphics... => 46080
['D',7] generating graphics... => 26880
['E',7] generating graphics... => 161280
['A',8] generating graphics... => 40320
['B',8] generating graphics... => 645120
click to show generating function       
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