A385041 Number of isomorphism classes of virtual quandles of order n.

1, 1, 2, 8, 26, 104, 467, 2540, 18419

Offset: 0

Author

Luc Ta, Jun 16 2025

Keywords

• nonn
• hard
• more

Comments

A virtual quandle is a quandle equipped with a distinguished quandle automorphism. Two virtual quandles (Q1,f1), (Q2,f2) are isomorphic if there exists a quandle isomorphism g: Q1 -> Q2 such that g*f1 = f2*g.

Links

• Alessia Cattabriga and Timur Nasybullov, Virtual quandle for links in lens spaces, RACSAM, 112 (2008), no. 3, 657-669.
• Vassily Olegovich Manturov, On invariants of virtual links, Acta Applicandae Mathematicae, 72 (2002), no. 3, 295-309.
• Lực Ta, Virtual-Rack Classification, GitHub, 2025.
• Lực Ta, Enumeration of virtual quandles up to isomorphism, arXiv:2506.16536 [math.GT], 2025. See p. 5.

Crossrefs

Cf. A385040, A383145, A181769, A181770.

Other 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, A383828-A383831, A383145, A383146, A178432

Programs

GAP

See Ta, GitHub link

Extensions

a(4)-a(8) corrected by Luc Ta, Jul 05 2025