Identifier
Identifier
Values
['A',1] generating graphics... => 2
['A',2] generating graphics... => 3
['B',2] generating graphics... => 4
['G',2] generating graphics... => 6
['A',3] generating graphics... => 4
['B',3] generating graphics... => 6
['C',3] generating graphics... => 6
['A',4] generating graphics... => 5
['B',4] generating graphics... => 8
['C',4] generating graphics... => 8
['D',4] generating graphics... => 6
['F',4] generating graphics... => 12
['A',5] generating graphics... => 6
['B',5] generating graphics... => 10
['C',5] generating graphics... => 10
['D',5] generating graphics... => 8
['A',6] generating graphics... => 7
['B',6] generating graphics... => 12
['C',6] generating graphics... => 12
['D',6] generating graphics... => 10
['E',6] generating graphics... => 12
['A',7] generating graphics... => 8
['B',7] generating graphics... => 14
['C',7] generating graphics... => 14
['D',7] generating graphics... => 12
['E',7] generating graphics... => 18
['A',8] generating graphics... => 9
['B',8] generating graphics... => 16
['C',8] generating graphics... => 16
['D',8] generating graphics... => 14
['E',8] generating graphics... => 30
['A',9] generating graphics... => 10
['B',9] generating graphics... => 18
['C',9] generating graphics... => 18
['D',9] generating graphics... => 16
['A',10] generating graphics... => 11
['B',10] generating graphics... => 20
['C',10] generating graphics... => 20
['D',10] generating graphics... => 18
click to show generating function       
Description
The Coxeter number of a finite Cartan type.
The Coxeter number $h$ for the Weyl group $W$ of the given finite Cartan type is defined as the order of the product of the Coxeter generators of $W$. Equivalently, this is equal to the maximal degree of a fundamental invariant of $W$, see also St000138The Catalan number of an irreducible finite Cartan type..
References
[1] Humphreys, J. E. Reflection groups and Coxeter groups MathSciNet:1066460
Code
def statistic(cartan_type):
    return prod(WeylGroup(cartan_type).gens()).order()
Created
Jun 24, 2013 at 12:53 by Christian Stump
Updated
Jun 01, 2015 at 17:58 by Martin Rubey