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Identifier
Values
['A',1] => 2
['A',2] => 4
['B',2] => 5
['G',2] => 7
['A',3] => 9
['B',3] => 16
['C',3] => 16
['A',4] => 16
['B',4] => 54
['C',4] => 54
['D',4] => 27
['F',4] => 78
['A',5] => 29
['B',5] => 140
['C',5] => 140
['D',5] => 78
['A',6] => 55
['A',7] => 137
['A',8] => 241
['A',9] => 453
['A',10] => 894
['A',11] => 2065
['A',12] => 3845
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Description
The number of non-isomorphic subgroups of the Weyl group of a finite Cartan type.
This statistic returns the number of non-isomorphic abstract groups.
See St001155The number of conjugacy classes of subgroups of the Weyl group of given type. for the number of conjugacy classes of subgroups.
References
[1] The number of isomorphism classes of subgroups of the symmetric group S_n. OEIS:A174511
Code
def statistic(ct):
    l = []
    for H in WeylGroup(ct).conjugacy_classes_subgroups():
        if not any(F.is_isomorphic(H) for F in l):
            l.append(H)
    return len(l)
Created
Apr 23, 2024 at 11:06 by Martin Rubey
Updated
Aug 04, 2024 at 22:05 by Martin Rubey