Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>2 ['A',2]=>4 ['B',2]=>6 ['G',2]=>8 ['A',3]=>10 ['B',3]=>20 ['C',3]=>20 ['A',4]=>26 ['B',4]=>76 ['C',4]=>76 ['D',4]=>44 ['F',4]=>140 ['A',5]=>76 ['B',5]=>312 ['C',5]=>312 ['D',5]=>156 ['A',6]=>232 ['B',6]=>1384 ['C',6]=>1384 ['D',6]=>752
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Description
The number of involutions in the Weyl group of a given Cartan type.
For type $A_n$, the generating function is $\exp(x+x^2/2)$, for type $BC_n$ it is $\exp(x^2+2x)$ and for type $D_n$ it is $\exp(x^2)(\exp(2x)+1)/2$.
Code
def statistic(C):
return sum(1 for x in WeylGroup(C) if x == x.inverse())

Created
Sep 02, 2019 at 14:20 by Martin Rubey
Updated
Sep 02, 2019 at 14:20 by Martin Rubey