**Identifier**

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

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 $\exp(x^2)(\exp(2x)+1)/2$.

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**searching the database

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