**Identifier**

Identifier

Values

['D',9]
=>
5040

['D',10]
=>
5040

['D',11]
=>
55440

['A',1]
=>
2

['A',2]
=>
6

['B',2]
=>
4

['G',2]
=>
6

['A',3]
=>
12

['B',3]
=>
12

['C',3]
=>
12

['A',4]
=>
60

['B',4]
=>
24

['C',4]
=>
24

['D',4]
=>
12

['F',4]
=>
24

['A',5]
=>
60

['B',5]
=>
120

['C',5]
=>
120

['D',5]
=>
120

['A',6]
=>
420

['B',6]
=>
120

['C',6]
=>
120

['D',6]
=>
120

['E',6]
=>
360

['A',7]
=>
840

['B',7]
=>
840

['C',7]
=>
840

['D',7]
=>
840

['E',7]
=>
2520

['A',8]
=>
2520

['B',8]
=>
1680

['C',8]
=>
1680

['D',8]
=>
840

['E',8]
=>
2520

Description

The exponent of the Weyl group of given type.

This is the least common multiple of the orders of the elements of the group.

In a comment to [4], see also [5], it is asked whether this is the same as the least common multiple of the degrees of the Weyl group.

This is the least common multiple of the orders of the elements of the group.

In a comment to [4], see also [5], it is asked whether this is the same as the least common multiple of the degrees of the Weyl group.

References

[1] groupprops:Exponent_of_a_group

[2]

[3]

[4]

[5]

[2]

*Least common multiple (or LCM) of 1, 2, ..., n for n >= 1, a(0) = 1.*OEIS:A003418[3]

*Least common multiple of 2, 4, 6, ..., 2n.*OEIS:A051426[4]

**user66288***The maximal order of an element in a Coxeter group*MathOverflow:343118[5]

**user66288***The least common multiple of all degrees of a finite Coxeter group and indecomposable elements in the generalized cycle decomposition*MathOverflow:345908Code

def statistic(C): return WeylGroup(C).as_permutation_group().exponent() # conjecturally def statistic(C): return lcm(WeylGroup(C).degrees())

Created

Apr 22, 2018 at 15:19 by

**Martin Rubey**Updated

Nov 13, 2019 at 10:37 by

**Martin Rubey**searching the database

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