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Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>4 ['A',2]=>8 ['B',2]=>22 ['G',2]=>32 ['A',3]=>21 ['B',3]=>84 ['C',3]=>84 ['A',4]=>39 ['B',4]=>325 ['C',4]=>325 ['D',4]=>146 ['F',4]=>441 ['A',5]=>92 ['B',5]=>1096 ['C',5]=>1096 ['D',5]=>274 ['A',6]=>170 ['B',6]=>3632 ['C',6]=>3632 ['D',6]=>1216 ['E',6]=>448 ['A',7]=>360 ['B',7]=>11184 ['C',7]=>11184 ['D',7]=>2796
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Description
The number conjugacy classes of pairs of commuting elements in the Weyl group of given Cartan type.
For any finite group $G$, this statistic is the cardinality of the set
$$ \{ c(a_1,a_2) \ | \ a_1,a_2 \in G \text{ with } a_1a_2 = a_2a_1\}, $$
where $c(a_1,a_2) = \{ (ga_1g^{-1},ga_2g^{-1}) \ | \ g \in G \}.$
References
[1] (reference broken) mathoverflow 468354
Code
def statistic(ct):
    G = WeylGroup(ct)
    r = 0
    for c in G.conjugacy_classes_representatives():
        C = G.centralizer(c)
        r += len(C.conjugacy_classes())
    return r
Created
Apr 05, 2024 at 11:43 by Martin Rubey
Updated
Apr 05, 2024 at 11:43 by Martin Rubey