**Identifier**

Identifier

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

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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