**Identifier**

Identifier

Values

['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

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.

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:3623739Code

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**searching the database

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