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.
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