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Identifier
Values
['A',1] => 1
['A',2] => 2
['B',2] => 2
['G',2] => 2
['A',3] => 6
['B',3] => 8
['C',3] => 8
['A',4] => 20
['B',4] => 48
['C',4] => 48
['D',4] => 32
['F',4] => 96
['A',5] => 240
['B',5] => 320
['C',5] => 320
['D',5] => 160
['A',6] => 420
['B',6] => 7680
['C',6] => 7680
['D',6] => 1920
['E',6] => 8640
['A',7] => 2688
['B',7] => 26880
['C',7] => 26880
['D',7] => 13440
['E',7] => 96768
['A',8] => 18144
['B',8] => 516096
['C',8] => 516096
['D',8] => 172032
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Description
The number of elements of maximal order in the Weyl group of a finite Cartan type.
For the symmetric group $\mathfrak S_n$ this is OEIS:A074859.
Code
def statistic(ct):
    l = [pi.order() for pi in WeylGroup(ct, implementation="permutation")]
    m = max(l)
    return sum(Integer(1) for e in l if e == m)
Created
Dec 12, 2021 at 21:05 by Martin Rubey
Updated
Dec 12, 2021 at 21:05 by Martin Rubey