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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
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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.
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