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

search for individual values

searching the database for the individual values of this statistic

/
search for generating function
searching the database for statistics with the same 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 $\exp(x^2)(\exp(2x)+1)/2$.

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

Sorry, this statistic was not found in the database

or

add this statistic to the database – it's very simple and we need your support!