A179010 -id:A179010

Search: a179010 -id:a179010

Displaying 1-2 of 2 results found.

page 1

A181769

Number of isomorphism classes of quandles of order n.

+10
8

1, 1, 1, 3, 7, 22, 73, 298, 1581, 11079, 102771, 1275419, 21101335, 469250886

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

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.

LINKS

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

CROSSREFS

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

KEYWORD

nonn,hard,more

AUTHOR

James McCarron

EXTENSIONS

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

STATUS

approved

A165200

Number of isomorphism classes of abelian / medial quandles.

+10
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 magma

CROSSREFS

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

KEYWORD

nonn,hard,more