A385040 -id:A385040 - cp's OEIS frontend

A181770 Number of isomorphism classes of racks of order n.

Original entry on oeis.org

1, 1, 2, 6, 19, 74, 353, 2080, 16023, 159526, 2093244, 36265070, 836395102, 25794670618

Offset: 0

James McCarron

Also the number of isomorphism classes of Legendrian racks of order n; see Ta, "Good involutions...," Theorem 10.1.

Also the number of isomorphism classes of GL-quandles of order n; see Ta, "Classification and...," Theorem 5.6.

Přemysl Jedlička, Agata Pilitowska, and Anna Zamojska-Dzienio, Multipermutation set theoretic solutions of the Yang-Baxter equation of level 2, arXiv:1901.01471 [math.QA], 2019.
Sam Nelson, Quandles and Racks
Lực Ta, Good involutions of conjugation subquandles, arXiv:2505.08090 [math.GT], 2025.
Lực Ta, Classification and structure of generalized Legendrian racks, arXiv:2504.12671 [math.GT], 2025.
Petr Vojtěchovský and Seung Yeop Yang, Enumeration of racks and quandles up to isomorphism, Mathematics of Computation, 88 (2019), 2523-2540; arXiv:1911.04991 [math.QA], 2019.

Cf. A181769, A383144-A383146, A383828-A383831, A385040, A385041, A386231-A386234.

a(9)-a(13) from Petr Vojtěchovský and Seung Yeop Yang added by Andrey Zabolotskiy, Jun 15 2022

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

Original entry on oeis.org

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

Offset: 0

Luc Ta, Jun 16 2025

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.

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. 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

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

cp's OEIS Frontend

A181770 Number of isomorphism classes of racks of order n.

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