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Identifier
Values
['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