cp's OEIS Frontend

A383828 Number of involutory racks of order n, up to isomorphism.

%I A383828 #9 May 16 2025 14:33:58
%S A383828 1,1,2,5,13,42,180,906,6317
%N A383828 Number of involutory racks of order n, up to isomorphism.
%C A383828 A rack is involutory if it satisfies the identity y(yx) = x. In particular, involutory quandles are called kei.
%C A383828 a(n) is also the number of Legendrian kei (i.e., kei equipped with Legendrian structures) up to order n up to isomorphism; see Ta, Theorem 1.1.
%C A383828 a(n) is also the number of symmetric kei (i.e., kei equipped with good involutions) up to order n up to isomorphism; see Ta, "Equivalences of...," Corollary 1.3.
%D A383828 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 A383828 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 A383828 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 A383828 Lực Ta, <a href="https://github.com/luc-ta/GL-Rack-Classification">GL-Rack Classification</a>, GitHub, 2025.
%o A383828 (GAP) # See Ta, GitHub link
%Y A383828 Cf. A383829-A383831, A383145, A383146, A181769, A181770, A178432.
%Y A383828 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 A383828 Sequences related to Legendrian knots: A374939, A374942, A374943, A374944, A374945, A374946, A374947.
%K A383828 nonn,hard,more
%O A383828 0,3
%A A383828 _Luc Ta_, May 11 2025