A383145 -id:A383145 - cp's OEIS frontend

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

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

Offset: 0

Luc Ta, Jun 16 2025

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.

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.

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

GAP
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See Ta, GitHub link
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a(4)-a(8) corrected by Luc Ta, Jul 05 2025

cp's OEIS Frontend

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

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