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Identifier
Values
['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