- FindStat

Identifier

St001750: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['A',1]=>0
['A',2]=>2
['B',2]=>5
['G',2]=>8
['A',3]=>6
['B',3]=>24
['C',3]=>24
['A',4]=>16
['B',4]=>224
['C',4]=>224
['D',4]=>69
['F',4]=>381
['A',5]=>44
['B',5]=>652
['C',5]=>652
['D',5]=>163
['A',6]=>90
['B',6]=>2165
['C',6]=>2165
['D',6]=>741
['E',6]=>372
['A',7]=>266
['B',7]=>6312
['C',7]=>6312
['D',7]=>1578
['E',7]=>1908
['A',8]=>508
['B',8]=>25761
['C',8]=>25761
['D',8]=>7304
['E',8]=>9108
                    

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Description

The number of even entries in the character table of the Weyl group of a Cartan type.

Code

def character_table(ct):
    G = WeylGroup(ct, implementation="permutation").gap()
    m = matrix([r.ValuesOfClassFunction().sage() for r in G.Irr()])
    return m

def statistic(ct):
    return sum(1 for e in character_table(ct).list() if is_even(e))

Created

Nov 29, 2021 at 10:57 by Martin Rubey

Updated

Nov 29, 2021 at 10:57 by Martin Rubey