edit this statistic or download as text // json
Identifier
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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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