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 A383146 #10 May 16 2025 09:45:32 %S A383146 1,1,4,13,61,298,2087,16941,187160 %N A383146 Number of medial GL-racks of order n, up to isomorphism. %C A383146 Generalized Legendrian racks, also called GL-racks or bi-Legendrian racks, are racks equipped with a rack automorphism that commutes with all inner rack automorphisms; see Ta, Definition 3.1 and Proposition 3.12. They are used to distinguish Legendrian links in contact three-space. %C A383146 GL-racks are precisely virtual racks in which all inner rack automorphisms are virtual rack automorphisms; cf. Cattabriga and Nasybullov, Section 3.2. %C A383146 A rack or quandle X is medial (also called abelian) if the map X x X -> X defined by (x,y) -> y(x) is a rack homomorphism. Equivalently, the identity (xy)(uv)=(xu)(yv) holds for all elements x, y, u, and v in X. %H A383146 Alessia Cattabriga and Timur Nasybullov, <a href="https://doi.org/10.1007/s13398-017-0445-0">Virtual quandle for links in lens spaces</a>, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A. Matemáticas, 112 (2018), no. 3, 657-669. %H A383146 Biswadeep Karmakar, Deepanshi Saraf, and Mahender Singh, <a href="http://arxiv.org/abs/2301.06854">Generalised Legendrian racks of Legendrian links</a>, arXiv: 2301.06854 [math.GT], 2023. %H A383146 Naoki Kimura, <a href="https://doi.org/10.1007/s13398-017-0445-0">Bi-Legendrian rack colorings of Legendrian knots</a>, Journal of Knot Theory and its Ramifications, 32 (2023), no. 4, Paper No. 2350029. %H A383146 Lực Ta, <a href="https://arxiv.org/abs/2504.12671">Generalized Legendrian racks: Classification, tensors, and knot coloring invariants</a>, arXiv: 2504.12671 [math.GT], 2025. %H A383146 Lực Ta, <a href="https://github.com/luc-ta/GL-Rack-Classification">GL-Rack Classification</a>, GitHub, 2025. %o A383146 (GAP) # see Ta, GitHub link %Y A383146 Cf. A383145. %Y A383146 Sequences related to medial racks and quandles: A383144, A165200, A242044, A226193, A242275, A243931, A257351. %Y A383146 Other sequences related to racks and quandles: A181769, A181770, A181771, A176077, A178432, A179010, A193024, A254434, A177886, A196111, A226173, A236146, A248908, A198147, A225744, A226172, A226174. %Y A383146 Sequences related to Legendrian knots: A374939, A374942, A374943, A374944, A374945, A374946, A374947. %K A383146 hard,more,nonn %O A383146 0,3 %A A383146 _Luc Ta_, Apr 17 2025