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

1,9

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

Table of n, a(n) for n=1..47.

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.

Sequence in context: A114118 A146014 A344824 * A212633 A202241 A248156

Adjacent sequences: A226170 A226171 A226172 * A226174 A226175 A226176

Keyword

nonn,more,hard

Author

W. Edwin Clark, May 29 2013

Extensions

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

Status

approved