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A165200 Number of isomorphism classes of abelian / medial quandles. 4
1, 1, 1, 3, 6, 18, 58, 251, 1410, 10311, 98577, 1246488, 20837439, 466087635 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Cf. A179010 (commutative quandles).

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

Added comment and link to indicate that magmas satisfying the identity

(XY)(UV) = (XU)(YV) in some circles are said to be "medial" as opposed to the term "abelian" used by the author of the sequence.

More terms from David Stanovsky, Sep 30 2014

Description edited by David Stanovsky, Sep 30 2014

STATUS

approved

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Last modified October 20 08:31 EDT 2019. Contains 328253 sequences. (Running on oeis4.)