A165200 - OEIS

A165200

Number of isomorphism classes of abelian / medial quandles.

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

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OFFSET

0,4

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

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

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.

Sequence in context: A215455 A211894 A173109 * A215635 A215634 A178789

Adjacent sequences: A165197 A165198 A165199 * A165201 A165202 A165203

KEYWORD

nonn,hard,more

AUTHOR

James McCarron, Jan 12 2011

EXTENSIONS

More terms from David Stanovsky, Sep 30 2014

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

STATUS

approved