## Cayley graphs for finite N-quandles

Below is a *Mathematica* program to generate the Cayley graph of a finite *N*-quandle, based on an algorithm due to Winker. The program was used for the following paper:

*N*-quandles of links, by Blake Mellor and Riley Smith

**Abstract:** The fundamental quandle is a powerful invariant of knots and links, but it is difficult to describe in detail. It is often useful to look at quotients of the quandle, especially finite quotients. One natural quotient introduced by Joyce is the *n*-quandle. Hoste and Shanahan gave a complete list of the knots and links which have finite *n*-quandles. We introduce a generalization of *n*-quandles for links, denoted *N*-quandles (for a link with *k* components, *N* is a *k*-tuple of positive integers), and we conjecture a classification of the links with finite *N*-quandles.

*Mathematica* program: NQCayleyGraph.nb

Comments and questions may be sent to blake.mellor@lmu.edu. You are welcome to use and modify the code as you wish - but if you add any cool features, please share them with me!

Return to Research.

Return to Blake's Homepage.