A226173 The number of connected keis (involutory quandles) of order n.

1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 3, 1, 0, 4, 0, 1, 3, 1, 3, 4, 0, 1, 10, 2, 0, 8, 2, 1, 10, 1, 0, 2, 0, 1, 16, 1, 0, 2, 8, 1, 8, 1, 0, 13, 0, 1

Offset: 1

Author

W. Edwin Clark, May 29 2013

Keywords

• nonn
• more
• hard

Comments

A quandle (Q,*) is a kei (also called involutory quandle) if for all x,y in Q we have (x*y)*y = x, that is, all right translations R_a: x-> x*a, are involutions.

References

• J. S. Carter, A survey of quandle ideas. in: Kauffman, Louis H. (ed.) et al., Introductory lectures on knot theory, Series on Knots and Everything 46, World Scientific (2012), 22--53.
• W. E. Clark, M. Elhamdadi, M. Saito and T. Yeatman, Quandle colorings of knots and applications. J. Knot Theory Ramifications 23/6 (2014), 1450035.

Links

• N. Andruskiewitsch, M. Graňa, From racks to pointed Hopf algebras, Adv. Math. 178/2 (2003), 177-243.
• J. Scott Carter, A Survey of Quandle Ideas, arXiv:1002.4429 [math.GT], Feb 2010
• W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman, Quandle Colorings of Knots and Applications, arXiv preprint arXiv:1312.3307, 2013
• A. Hulpke, D. Stanovský, P. Vojtěchovský, Connected quandles and transitive groups, arXiv:1409.2249 [math.GR], Sep 2014, to appear in J. Pure Appl. Algebra.

Crossrefs

Cf. A181771 (number of connected quandles of order n).

See also Index to OEIS under quandles.

Extensions

a(36)-a(47) (calculated by methods described in Hulpke, Stanovský, Vojtěchovský link) from David Stanovsky, Jun 02 2015