New upper bounds for stick numbers

Journal of Knot Theory and Its Ramifications, vol. 35

Abstract

We use a version of simulated annealing with knot-type preserving moves to find polygonal representatives of various knot types with low stick number. These give better bounds on stick numbers of prime knots through 10 crossings, and for the first time give a comprehensive table of stick number bounds on all knots through 13 crossings. These are equal to existing lower bounds (and hence determine the stick number exactly) for 19 knot types whose exact stick number was not known previously.

Authors 3

1. Jason Cantarella

   University of Georgia

   Affiliation as printed

   Mathematics Department, University of Georgia, Athens, GA, USA

2. Andrew Rechnitzer

   University of British Columbia

   Affiliation as printed

   Mathematics Department, University of British Columbia, Vancouver, BC, Canada

3. Clayton Shonkwiler

   Colorado State University

   Affiliation as printed

   Department of Mathematics, Colorado State University, Fort Collins, CO, USA