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Statistic identifier: St001748

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Collection: Finite Cartan types

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Description: The number of negative entries in the character table of the Weyl group of a Cartan type.

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References: 

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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 sum(1 for v in character_table(ct).list() if v < 0)


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Statistic values:

['A',1] => 1
['A',2] => 2
['B',2] => 7
['G',2] => 12
['A',3] => 7
['B',3] => 35
['C',3] => 35
['A',4] => 13
['B',4] => 111
['C',4] => 111
['D',4] => 51
['F',4] => 160
['A',5] => 34
['B',5] => 427
['C',5] => 427
['D',5] => 94
['A',6] => 72
['B',6] => 1303
['C',6] => 1303
['D',6] => 408
['E',6] => 166
['A',7] => 137
['B',7] => 4015
['C',7] => 4015
['D',7] => 960
['E',7] => 1096
['A',8] => 249
['B',8] => 9655
['C',8] => 9655
['D',8] => 2684
['E',8] => 3200

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Created: Nov 29, 2021 at 09:56 by Martin Rubey

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Last Updated: Nov 29, 2021 at 09:56 by Martin Rubey