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A181769 Number of isomorphism classes of quandles of order n. 8
1, 1, 1, 3, 7, 22, 73, 298, 1581, 11079, 102771, 1275419, 21101335, 469250886 (list; graph; refs; listen; history; text; internal format)



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.


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

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


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

Sequence in context: A045610 A259809 A340022 * A354771 A075214 A070766

Adjacent sequences: A181766 A181767 A181768 * A181770 A181771 A181772




James McCarron


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



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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)