**Identifier**

Identifier

Values

['A',1]
=>
1

['A',2]
=>
1

['B',2]
=>
2

['G',2]
=>
2

['A',3]
=>
1

['B',3]
=>
2

['C',3]
=>
2

['A',4]
=>
1

['B',4]
=>
2

['C',4]
=>
2

['D',4]
=>
1

['F',4]
=>
2

['A',5]
=>
1

['B',5]
=>
2

['C',5]
=>
2

['D',5]
=>
1

['A',6]
=>
1

['B',6]
=>
2

['C',6]
=>
2

['D',6]
=>
1

['E',6]
=>
1

['A',7]
=>
1

['B',7]
=>
2

['C',7]
=>
2

['D',7]
=>
1

['E',7]
=>
1

['A',8]
=>
1

['B',8]
=>
2

['C',8]
=>
2

['D',8]
=>
1

['E',8]
=>
1

Description

The number of orbits of reflections of a finite Cartan type.

Let $W$ be the Weyl group of a Cartan type. The reflections in $W$ are closed under conjugation, and this statistic counts the number of conjugacy classes of $W$ that are reflections.

It is well-known that there are either one or two such conjugacy classes.

Let $W$ be the Weyl group of a Cartan type. The reflections in $W$ are closed under conjugation, and this statistic counts the number of conjugacy classes of $W$ that are reflections.

It is well-known that there are either one or two such conjugacy classes.

Code

def statistic(cartan_type): W = ReflectionGroup(cartan_type) return sum( 1 for w in W.conjugacy_classes_representatives() if w.is_reflection() )

Created

Jun 25, 2017 at 10:15 by

**Christian Stump**Updated

Jun 25, 2017 at 10:15 by

**Christian Stump**searching the database

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