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Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>1 ['A',2]=>5 ['B',2]=>10 ['G',2]=>26 ['A',3]=>14 ['B',3]=>35 ['C',3]=>35 ['A',4]=>30 ['B',4]=>84 ['C',4]=>84 ['D',4]=>44 ['F',4]=>196 ['A',5]=>55 ['B',5]=>165 ['C',5]=>165 ['D',5]=>100 ['A',6]=>91 ['B',6]=>286 ['C',6]=>286 ['D',6]=>190 ['E',6]=>276 ['A',7]=>140 ['B',7]=>455 ['C',7]=>455 ['D',7]=>322 ['E',7]=>735 ['A',8]=>204 ['B',8]=>680 ['C',8]=>680 ['D',8]=>504 ['E',8]=>2360
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Description
The sum of the squares of the exponents of the Weyl group of the finite Cartan type.
According to Suter [1], this equals $\frac{1}{6}n(h^2 + \gamma - h)$, where $n$ is the rank, $h$ is the Coxeter number and $\gamma$ the gamma number.
References
[1] Suter, R. Coxeter and dual Coxeter numbers MathSciNet:1600666
Code
def statistic(ct):
    return sum((d-1)^2 for d in WeylGroup(ct).degrees())
Created
Feb 06, 2021 at 23:20 by Martin Rubey
Updated
Feb 06, 2021 at 23:20 by Martin Rubey