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Identifier
Values
=>
Cc0022;cc-rep
['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