A181769 Number of isomorphism classes of quandles of order n.

1, 1, 1, 3, 7, 22, 73, 298, 1581, 11079, 102771, 1275419, 21101335, 469250886

Offset: 0

Author

James McCarron

Keywords

• nonn
• hard
• more

Comments

Quandles up to order 8 were determined first by Sam Nelson and co-authors (see references). Nelson's results were confirmed independently by the submitter, and extended to order 9.

Links

• M. Elhamdadi, Distributivity in Quandles and Quasigroups, arXiv preprint arXiv:1209.6518 [math.RA], 2012. - From _N. J. A. Sloane_, Dec 29 2012
• Richard Henderson, Todd Macedo and Sam Nelson, Symbolic Computation with Finite Quandles, J. Symb. Comp. 41 (2006), 811-817.
• Benita Ho and Sam Nelson, Matrices and Finite Quandles, Homology, Homotopy and Applications, 7 (2005), No. 1, 197-208.
• P. Jedlicka, A. Pilitowska, D. Stanovsky et al., The structure of medial quandles, arXiv preprint 1409.8396 [math.GR], 2014-2015.
• J. McCarron, Connected Quandles with Order Equal to Twice an Odd Prime, arXiv preprint arXiv:1210.2150 [math.GR], 2012. - From _N. J. A. Sloane_, Dec 31 2012
• Sam Nelson, Quandles and Racks
• Petr Vojtěchovský and Seung Yeop Yang, Enumeration of racks and quandles up to isomorphism, Math. Comp. 88 (2019), 2523-2540; arXiv:1911.04991 [math.QA], 2019.
• Wikipedia, Quandles
• Index entries for sequences related to quandles and racks

Crossrefs

Cf. A176077, A181771, A165200, A179010, A177886, A178432, A181770.

Extensions

a(10)-a(13) from Petr Vojtěchovský and Seung Yeop Yang added by Andrei Zabolotskii, Jun 15 2022