Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Friday, Oct, 12, 2012 , at U. of Waterloo
Small Homogeneous Quandles
James McCarron, Maplesoft

Abstract: We derive an algorithm for computing all the homogeneous quandles of a given order n provided that a list of the transitive permutation groups of degree n are known. We discuss the implementation of the algorithm, and use it to enumerate the number of isomorphism classes of homogeneous quandles up to order 23 and compute representatives for each class. We also completely determine the homogeneous quandles of prime order. As a by-product, we are able to replicate an earlier calculation of the connected quandles of order at most 30 and, based on this, to compute the number of isomorphism classes of simple quandles to the same order.

 

Last modified on Wednesday, 07 November 2012, at 17:14 hours.