Identifier
- St001945: Finite Cartan types ⟶ ℤ
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.
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] oeis:A174511
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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
Apr 23, 2024 at 11:33 by Martin Rubey
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