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Statistic identifier: St000857

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Collection: Finite Cartan types

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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.

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References: 

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Code:
def statistic(cartan_type):
    W = ReflectionGroup(cartan_type)
    return W.rank() * W.coxeter_number() / 2

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Statistic values:

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

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