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Number of isomorphism classes of abelian / medial quandles.
4

%I #41 Jun 15 2022 04:09:28

%S 1,1,1,3,6,18,58,251,1410,10311,98577,1246488,20837439,466087635

%N Number of isomorphism classes of abelian / medial quandles.

%C A quandle is abelian / medial (both names are being used) if it satisfies the identity (XY)(UV) = (XU)(YV). Not to be confused with a commutative quandle (A179010).

%H P. Jedlička, A. Pilitowska, D. Stanovský, A. Zamojska-Dzienio, <a href="http://arxiv.org/abs/1409.8396">The structure of medial quandles</a>, arXiv preprint 1409.8396 [math.GR], 2014.

%H David Joyce, <a href="http://dx.doi.org/10.1016/0022-4049(82)90077-9">A classifying invariant of knots, the knot quandle</a>, J. Pure Appl. Algebra 23 (1982) 37-65.

%H Sam Nelson, <a href="http://www1.cmc.edu/pages/faculty/VNelson/quandles.html">Quandles and Racks</a>

%H David Stanovský, <a href="http://www.karlin.mff.cuni.cz/~stanovsk/quandles/">Calculating with quandles</a>, GAP code to calculate the numbers.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Quandles">Quandles</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Medial_magma">Medial magma</a>

%Y Cf. A179010 (commutative quandles), A242044, A242275.

%K nonn,hard,more

%O 0,4

%A _James McCarron_, Jan 12 2011

%E More terms from _David Stanovsky_, Sep 30 2014

%E Description edited by _W. Edwin Clark_, May 30 2013, and _David Stanovsky_, Sep 30 2014