This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371059 #48 Mar 19 2024 12:43:08
%S A371059 1,1,9,14,22,44,74,160,256,462,817,1494,2543,4427,7699,13352,22616,
%T A371059 38610,65052,110004,182961,305007,503299,830648,1356227,2212790,
%U A371059 3583419,5790836
%N A371059 Number of conjugacy classes of pairs of commuting elements in the alternating group A_n.
%C A371059 The number of conjugacy classes of pairs of commuting elements in a finite group G is the cardinality of the set {c(a,b) | a,b in G and ab=ba} where c(a,b) = {(gag^(-1),gbg^(-1)) | g in G}.
%C A371059 It is equal to the number of conjugacy classes within the centralizers of class representatives of G.
%C A371059 This reformulation was employed in the sequence-generating program.
%C A371059 It is also equal to the rank of the modular fusion category Z(Rep(G)), the Drinfeld center of Rep(G).
%C A371059 These reformulations are explained in the linked MathOverflow posts.
%D A371059 A. Davydov, Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds. J. Math. Phys. 55 (2014), no. 9, 092305, 13 pp.
%H A371059 Sébastien Palcoux, <a href="https://mathoverflow.net/q/466800/34538">Number of conjugacy classes of pairs of commuting elements</a>, MathOverflow.
%H A371059 Sébastien Palcoux, <a href="https://mathoverflow.net/q/466864/34538">Is the rank of an integral MTC an upper bound for the prime factors of its FPdim?</a>, MathOverflow.
%o A371059 (GAP)
%o A371059 List([1..10],n->Sum(List(ConjugacyClasses(AlternatingGroup(n)),c->NrConjugacyClasses(Centralizer(AlternatingGroup(n),Representative(c))))));
%Y A371059 Cf. A000702.
%K A371059 nonn,more
%O A371059 1,3
%A A371059 _Sébastien Palcoux_, Mar 11 2024