login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A226172 The number of faithful connected quandles of order n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
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.
Sequence in context: A133945 A124219 A103833 * A281006 A046227 A120842
KEYWORD
nonn,more,hard
AUTHOR
W. Edwin Clark, May 29 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)