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Identifier
Values
['A',1] => 2
['A',2] => 3
['B',2] => 3
['G',2] => 4
['A',3] => 4
['B',3] => 5
['C',3] => 5
['A',4] => 6
['B',4] => 6
['C',4] => 6
['D',4] => 5
['F',4] => 7
['A',5] => 6
['B',5] => 9
['C',5] => 9
['D',5] => 8
['A',6] => 9
['B',6] => 9
['C',6] => 9
['D',6] => 9
['E',6] => 10
['A',7] => 11
['B',7] => 13
['C',7] => 13
['D',7] => 12
['E',7] => 15
['A',8] => 14
['B',8] => 16
['C',8] => 16
['D',8] => 15
['E',8] => 17
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Description
The number of distinct orders of elements in a Weyl group of finite Cartan type.
References
[1] Number of distinct orders of permutations of n objects; number of nonisomorphic cyclic subgroups of symmetric group S_n. OEIS:A009490
Code
def statistic(ct):
    return len(set(w.order() for w in WeylGroup(ct).conjugacy_classes_representatives()))
Created
Jul 09, 2024 at 12:05 by Martin Rubey
Updated
Aug 04, 2024 at 22:05 by Martin Rubey