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URL: https://oeis.org/A383830

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A383830
Number of Legendrian quandles of order n, up to isomorphism.
2
1, 1, 2, 5, 15, 54, 240, 1306, 9477
OFFSET
0,3
COMMENTS
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.
a(n) is also the number of racks X such that the kink map X -> X defined by x -> x(x) is an involution; see Ta, "Equivalences of...," Theorem 1.1.
LINKS
Jose Ceniceros, Mohamed Elhamdadi, and Sam Nelson, Legendrian rack invariants of Legendrian knots, Communications of the Korean Mathematical Society, 36 (2021), no. 3, 623-639.
Lực Ta, Equivalences of racks, Legendrian racks, and symmetric racks, arXiv: 2505.08090 [math.GT], 2025.
Lực Ta, GL-Rack Classification, GitHub, 2025.
PROG
(GAP) # See Ta, GitHub link
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Luc Ta, May 11 2025
STATUS
approved