A226173 - OEIS

%I #31 Jun 02 2015 14:02:14

%S 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,

%T 0,1,16,1,0,2,8,1,8,1,0,13,0,1

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

%C 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.

%D 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.

%D W. E. Clark, M. Elhamdadi, M. Saito and T. Yeatman, Quandle colorings of knots and applications. J. Knot Theory Ramifications 23/6 (2014), 1450035.

%H N. Andruskiewitsch, M. Graňa, <a href="http://dx.doi.org/10.1016/S0001-8708(02)00071-3">From racks to pointed Hopf algebras</a>, Adv. Math. 178/2 (2003), 177-243.

%H J. Scott Carter, <a href="http://arxiv.org/abs/1002.4429">A Survey of Quandle Ideas</a>, arXiv:1002.4429 [math.GT], Feb 2010

%H W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman, <a href="http://arxiv.org/abs/1312.3307">Quandle Colorings of Knots and Applications</a>, arXiv preprint arXiv:1312.3307, 2013

%H A. Hulpke, D. Stanovský, P. Vojtěchovský, <a href="http://arxiv.org/abs/1409.2249">Connected quandles and transitive groups</a>, arXiv:1409.2249 [math.GR], Sep 2014, to appear in J. Pure Appl. Algebra.

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

%Y See also Index to OEIS under quandles.

%K nonn,more,hard

%O 1,9

%A _W. Edwin Clark_, May 29 2013

%E a(36)-a(47) (calculated by methods described in Hulpke, Stanovský, Vojtěchovský link) from _David Stanovsky_, Jun 02 2015