A181770 Number of isomorphism classes of racks of order n.

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

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..13.

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.

Crossrefs

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

Sequence in context: A361489 A378586 A268569 * A138800 A008989 A057240

Adjacent sequences: A181767 A181768 A181769 * A181771 A181772 A181773

Keyword

nonn,hard,more

Author

James McCarron

Extensions

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

Status

approved