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Identifier
Values
=>
Cc0022;cc-rep
['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 ['D',9]=>5040 ['D',10]=>5040 ['D',11]=>55440
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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.
References
[1] groupprops:Exponent_of_a_group
[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:345908
Code
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