cp's OEIS Frontend

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.

A386231 Number of symmetric racks of order n, up to isomorphism.

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%I A386231 #9 Jul 21 2025 17:49:12
%S A386231 1,1,4,9,42,154,1064,6678,73780
%N A386231 Number of symmetric racks of order n, up to isomorphism.
%C A386231 A good involution f of a rack R is an involution that commutes with all inner automorphisms and satisfies the identity f(y)(x) = y^-1(x). We call the pair (R,f) a symmetric rack. A symmetric rack isomorphism is a rack isomorphism that intertwines good involutions.
%D A386231 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 A386231 Lực Ta, <a href="https://arxiv.org/abs/2505.08090">Good involutions of conjugation subquandles</a>, arXiv:2505.08090 [math.GT], 2025. See Table 1.
%H A386231 Lực Ta, <a href="https://github.com/luc-ta/Symmetric-Rack-Classification">Symmetric-Rack-Classification</a>, GitHub, 2025.
%o A386231 (GAP) # See Ta, GitHub link
%Y A386231 Cf. A386232, A181770, A383828, A386233, A386234.
%Y A386231 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, A181769.
%K A386231 nonn,hard,more
%O A386231 0,3
%A A386231 _Luc Ta_, Jul 16 2025