- FindStat

Identifier

St001155: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['A',1]=>2
['A',2]=>4
['B',2]=>8
['G',2]=>10
['A',3]=>11
['B',3]=>33
['C',3]=>33
['A',4]=>19
['B',4]=>193
['C',4]=>193
['D',4]=>98
['F',4]=>246
['A',5]=>56
['B',5]=>953
['C',5]=>953
['D',5]=>197
['A',6]=>96
['B',6]=>7440
['C',6]=>7440
['D',6]=>1916
['E',6]=>350
['A',7]=>296
['A',8]=>554
['A',9]=>1593
['A',10]=>3094
                    

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Description

The number of conjugacy classes of subgroups of the Weyl group of given type.

References

[1] Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n. OEIS:A000638
[2] Number of conjugacy classes of subgroups of the hyperoctahedral group. OEIS:A269890

Code

def statistic(C):
    return len(WeylGroup(C).as_permutation_group().conjugacy_classes_subgroups())

Created

Apr 21, 2018 at 23:43 by Martin Rubey

Updated

Oct 18, 2020 at 17:52 by Martin Rubey