OFFSET
0,3
COMMENTS
A rack is involutory if it satisfies the identity y(yx) = x. In particular, involutory quandles are called kei.
A rack is medial if it satisfies the identity (xy)(uv) = (xu)(yv).
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.
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.
REFERENCES
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.
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
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.
KEYWORD
nonn,hard,more
AUTHOR
Luc Ta, May 11 2025
STATUS
approved
