- FindStat

Identifier

St001747: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['A',1]=>0
['A',2]=>1
['B',2]=>3
['G',2]=>4
['A',3]=>4
['B',3]=>16
['C',3]=>16
['A',4]=>10
['B',4]=>136
['C',4]=>136
['D',4]=>47
['F',4]=>239
['A',5]=>29
['B',5]=>340
['C',5]=>340
['D',5]=>85
['A',6]=>55
['B',6]=>1419
['C',6]=>1419
['D',6]=>453
['E',6]=>226
['A',7]=>153
['B',7]=>3720
['C',7]=>3720
['D',7]=>930
['E',7]=>1216
['A',8]=>307
['B',8]=>13969
['C',8]=>13969
['D',8]=>4158
['E',8]=>5696
                    

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Description

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

References

[1] Palcoux, S. The zero entries in the character table of a finite group MathOverflow:363796

Code

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

def statistic(ct):
    return character_table(ct).list().count(0)

Created

Nov 29, 2021 at 09:51 by Martin Rubey

Updated

Nov 29, 2021 at 09:51 by Martin Rubey