Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>2 ['A',2]=>3 ['B',2]=>4 ['G',2]=>6 ['A',3]=>4 ['B',3]=>6 ['C',3]=>6 ['A',4]=>5 ['B',4]=>8 ['C',4]=>8 ['D',4]=>6 ['F',4]=>12 ['A',5]=>6 ['B',5]=>10 ['C',5]=>10 ['D',5]=>8 ['A',6]=>7 ['B',6]=>12 ['C',6]=>12 ['D',6]=>10 ['E',6]=>12 ['A',7]=>8 ['B',7]=>14 ['C',7]=>14 ['D',7]=>12 ['E',7]=>18 ['A',8]=>9 ['B',8]=>16 ['C',8]=>16 ['D',8]=>14 ['E',8]=>30 ['A',9]=>10 ['B',9]=>18 ['C',9]=>18 ['D',9]=>16 ['A',10]=>11 ['B',10]=>20 ['C',10]=>20 ['D',10]=>18
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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