A165200 Number of isomorphism classes of abelian / medial quandles.

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

Offset: 0

Author

James McCarron, Jan 12 2011

Keywords

• nonn
• hard
• more

Comments

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).

Links

• P. Jedlička, A. Pilitowska, D. Stanovský, A. Zamojska-Dzienio, The structure of medial quandles, arXiv preprint 1409.8396 [math.GR], 2014.
• David Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37-65.
• Sam Nelson, Quandles and Racks
• David Stanovský, Calculating with quandles, GAP code to calculate the numbers.
• Wikipedia, Quandles
• Wikipedia, Medial magma

Crossrefs

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

Extensions

More terms from David Stanovsky, Sep 30 2014

Description edited by W. Edwin Clark, May 30 2013, and David Stanovsky, Sep 30 2014