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 A386233 #7 Jul 21 2025 17:50:02 %S A386233 1,32,1,17,1,13056,66,33,1,1 %N A386233 Number of good involutions of all nontrivial conjugation quandles of order A060652(n). %C A386233 A good involution f of a quandle Q is an involution that commutes with all inner automorphisms and satisfies the identity f(y)(x) = y^-1(x). We call the pair (Q,f) a symmetric quandle. %C A386233 A conjugation quandle is a group viewed as a quandle under the conjugation operation. Since conjugation quandles of abelian groups are trivial, this sequence only considers nonabelian groups. %D A386233 Seiichi Kamada, Quandles with good involutions, their homologies and knot invariants, Intelligence of Low Dimensional Topology 2006, World Scientific Publishing Co. Pte. Ltd., 2007, 101-108. %H A386233 Lực Ta, <a href="https://arxiv.org/abs/2505.08090">Good involutions of conjugation subquandles</a>, arXiv:2505.08090 [math.GT], 2025. See Table 2. %H A386233 Lực Ta, <a href="https://github.com/luc-ta/Symmetric-Rack-Classification">Symmetric-Rack-Classification</a>, GitHub, 2025. %e A386233 For n = 1, 3, 5, 9, 10, there is a unique nonabelian group G of order A060652(n), and G is centerless. It follows from Ta, Prop. 5.3 that a(n) = 1. %o A386233 (GAP) See Ta, GitHub link %Y A386233 Cf. A000001, A060652, A060689, A386233, A181769, A383828, A386231, A386232. %Y A386233 Other sequences related to racks and quandles: A383144, A181771, A176077, A179010, A193024, A254434, A177886, A196111, A226173, A236146, A248908, A165200, A242044, A226193, A242275, A243931, A257351, A198147, A225744, A226172, A226174, A383828-A383831, A383145, A383146, A178432, A385041, A383145, A181770. %K A386233 hard,more,nonn %O A386233 1,2 %A A386233 _Luc Ta_, Jul 16 2025