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.

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**searching the database

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