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 A383829 #8 May 16 2025 14:33:54 %S A383829 1,1,2,5,12,38,168,850,6090 %N A383829 Number of medial involutory racks of order n, up to isomorphism. %C A383829 A rack is involutory if it satisfies the identity y(yx) = x. In particular, involutory quandles are called kei. %C A383829 A rack is medial if it satisfies the identity (xy)(uv) = (xu)(yv). %C A383829 a(n) is also the number of medial Legendrian kei (i.e., medial kei equipped with Legendrian structures) up to order n up to isomorphism; see Ta, Theorem 1.1. %C A383829 a(n) is also the number of medial symmetric kei (i.e., medial kei equipped with good involutions) up to order n up to isomorphism; see Ta, "Equivalences of...," Corollary 1.3. %D A383829 Seiichi Kamada, Quandles with good involutions, their homologies and knot invariants, Intelligence of Low Dimensional Topology 2006, World Scientific Publishing Co. Pte. Ltd., 2007, pages 101-108. %H A383829 Jose Ceniceros, Mohamed Elhamdadi, and Sam Nelson, <a href="https://doi.org/10.4134/CKMS.c200251">Legendrian rack invariants of Legendrian knots</a>, Communications of the Korean Mathematical Society, 36 (2021), no. 3, 623-639. %H A383829 Lực Ta, <a href="https://arxiv.org/abs/2505.08090">Equivalences of racks, Legendrian racks, and symmetric racks</a>, arXiv: 2505.08090 [math.GT], 2025. %H A383829 Lực Ta, <a href="https://github.com/luc-ta/GL-Rack-Classification">GL-Rack Classification</a>, GitHub, 2025. %o A383829 (GAP) # See Ta, GitHub link %Y A383829 Cf. A383828, A383830, A383831, A383145, A383146, A181769, A181770, A178432. %Y A383829 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. %Y A383829 Sequences related to Legendrian knots: A374939, A374942, A374943, A374944, A374945, A374946, A374947. %K A383829 nonn,hard,more %O A383829 0,3 %A A383829 _Luc Ta_, May 11 2025