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Identifier
Values
=>
Cc0022;cc-rep
['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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Description
The number of negative entries in the character table of the Weyl group of a Cartan type.
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)
Created
Nov 29, 2021 at 09:56 by Martin Rubey
Updated
Nov 29, 2021 at 09:56 by Martin Rubey