- FindStat

Identifier

St001953: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['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