Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001944
Mapping
St001944: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['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
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 $c(a_1,a_2) = \{ (ga_1g^{-1},ga_2g^{-1}) \ | \ g \in G \}.$