A385040 Number of isomorphism classes of virtual racks of order n.

1, 1, 4, 15, 71, 350, 2372, 18543, 199491

Offset

0,3

Comments

A virtual rack is a rack equipped with a distinguished rack automorphism. Two virtual racks (R1,f1), (R2,f2) are isomorphic if there exists a rack isomorphism g: R1 -> R2 such that g*f1 = f2*g.

Links

Table of n, a(n) for n=0..8.

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.

Prog

(GAP) See Ta, GitHub link

Crossrefs

Cf. A385041, 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

Sequence in context: A366034 A027316 A085349 * A185133 A278640 A026992

Adjacent sequences: A385037 A385038 A385039 * A385041 A385042 A385043

Keyword

nonn,hard,more

Author

Luc Ta, Jun 16 2025

Extensions

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

Status

approved