Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>1 ['A',2]=>3 ['B',2]=>4 ['G',2]=>6 ['A',3]=>6 ['B',3]=>9 ['C',3]=>9 ['A',4]=>10 ['B',4]=>16 ['C',4]=>16 ['D',4]=>12 ['F',4]=>24 ['A',5]=>15 ['B',5]=>25 ['C',5]=>25 ['D',5]=>20 ['A',6]=>21 ['B',6]=>36 ['C',6]=>36 ['D',6]=>30 ['E',6]=>36 ['A',7]=>28 ['B',7]=>49 ['C',7]=>49 ['D',7]=>42 ['E',7]=>63 ['A',8]=>36 ['B',8]=>64 ['C',8]=>64 ['D',8]=>56 ['E',8]=>120
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Description
The number of reflections of the Weyl group of a finite Cartan type.
By the one-to-one correspondence between reflections and reflecting hyperplanes, this is also the number of reflecting hyperplanes. This is given by $nh/2$ where $n$ is the rank and $h$ is the Coxeter number.
Code
def statistic(cartan_type):
W = ReflectionGroup(cartan_type)
return W.rank() * W.coxeter_number() / 2

Created
Jun 25, 2017 at 09:45 by Christian Stump
Updated
Jun 25, 2017 at 09:45 by Christian Stump