A226172 The number of faithful connected quandles of order n.

1, 0, 1, 1, 3, 2, 5, 2, 8, 1, 9, 8, 11, 0, 7, 9, 15, 12, 17, 9, 9, 0, 21, 27, 34, 0, 62, 13, 27, 20, 29, 8, 11, 0, 15

Offset: 1

Author

W. Edwin Clark, May 29 2013

Keywords

• nonn
• more
• hard

Comments

Let Q be a quandle with product *. Let R_a: x ->x*a for a,x in Q. By definition R_a is an automorphism of the quandle Q. If the mapping a->R_a is an injection then the quandle is said to be faithful. A quandle is faithful precisely when the columns of the Cayley table of the quandle are distinct.

This sequence was computed using Leandro Vendramin's list of all connected quandles of order at most 35.

Warning: Vendramin's quandles are assumed to be left distributive and hence one must reverse the order of the product to get the (right distributive) quandles used by knot theorists.

Links

• W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman, Quandle Colorings of Knots and Applications, arXiv preprint arXiv:1312.3307, 2013
• F. J. B. J. Clauwens, Small Connected Quandles, arxiv 1011.2456, Nov 10 2010
• Leandro Vendramin, On the classification of quandles of low order, arXiv:1105.5341v1 [math.GT], May 26 2011

Crossrefs

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

See also Index to OEIS under quandles.