cp's OEIS Frontend

A383831 Number of medial Legendrian quandles of order n, up to isomorphism.

%I A383831 #11 May 16 2025 09:44:45
%S A383831 1,1,2,5,14,48,219,1207,9042
%N A383831 Number of medial Legendrian quandles of order n, up to isomorphism.
%C A383831 A rack or quandle is medial if it satisfies the identity (xy)(uv) = (xu)(yv).
%C A383831 A Legendrian quandle is a pair (X,u) where X is a quandle and u is an involutory automorphism of X such that u(yx)=y(u(x)); see Ta, "Generalized Legendrian...," Corollary 3.13.
%C A383831 a(n) is also the number of medial racks X such that the kink map X -> X defined by x -> x(x) is an involution; see Ta, "Equivalences of...," Theorem 1.1.
%H A383831 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 A383831 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 A383831 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 A383831 Lực Ta, <a href="https://github.com/luc-ta/GL-Rack-Classification">GL-Rack Classification</a>, GitHub, 2025.
%o A383831 (GAP) # See Ta, GitHub link
%Y A383831 Cf. A383828-A383830, A383145, A383146, A181769, A181770, A178432.
%Y A383831 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 A383831 Sequences related to Legendrian knots: A374939, A374942, A374943, A374944, A374945, A374946, A374947.
%K A383831 hard,more,nonn
%O A383831 0,3
%A A383831 _Luc Ta_, May 16 2025