Identifier
Identifier
Values
['A',1] generating graphics... => 2
['A',2] generating graphics... => 4
['B',2] generating graphics... => 6
['G',2] generating graphics... => 8
['A',3] generating graphics... => 10
['B',3] generating graphics... => 20
['C',3] generating graphics... => 20
['A',4] generating graphics... => 26
['B',4] generating graphics... => 76
['C',4] generating graphics... => 76
['D',4] generating graphics... => 44
['F',4] generating graphics... => 140
['A',5] generating graphics... => 76
['B',5] generating graphics... => 312
['C',5] generating graphics... => 312
['D',5] generating graphics... => 156
['A',6] generating graphics... => 232
['B',6] generating graphics... => 1384
['C',6] generating graphics... => 1384
['D',6] generating graphics... => 752
click to show generating function       
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