Identifier
Identifier
Values
['A',1] generating graphics... => 1
['A',2] generating graphics... => 3
['B',2] generating graphics... => 4
['G',2] generating graphics... => 6
['A',3] generating graphics... => 6
['B',3] generating graphics... => 9
['C',3] generating graphics... => 9
['A',4] generating graphics... => 10
['B',4] generating graphics... => 16
['C',4] generating graphics... => 16
['D',4] generating graphics... => 12
['F',4] generating graphics... => 24
['A',5] generating graphics... => 15
['B',5] generating graphics... => 25
['C',5] generating graphics... => 25
['D',5] generating graphics... => 20
['A',6] generating graphics... => 21
['B',6] generating graphics... => 36
['C',6] generating graphics... => 36
['D',6] generating graphics... => 30
['E',6] generating graphics... => 36
['A',7] generating graphics... => 28
['B',7] generating graphics... => 49
['C',7] generating graphics... => 49
['D',7] generating graphics... => 42
['E',7] generating graphics... => 63
['A',8] generating graphics... => 36
['B',8] generating graphics... => 64
['C',8] generating graphics... => 64
['D',8] generating graphics... => 56
['E',8] generating graphics... => 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