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Identifier
Values
=>
Cc0022;cc-rep
['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