The Shapes of Tight Composite Knots
Differential Geometry
2015-05-30 v1 Mathematical Physics
math.MP
Abstract
We present new computations of tight shapes obtained using the constrained gradient descent code RIDGERUNNER for 544 composite knots with 12 and fewer crossings, expanding our dataset to 943 knots and links. We use the new data set to analyze two outstanding conjectures about tight knots, namely that the ropelengths of composite knots are at least 4\pi-4 less than the sums of the prime factors and that the writhes of composite knots are the sums of the writhes of the prime factors.
Keywords
Cite
@article{arxiv.1110.3262,
title = {The Shapes of Tight Composite Knots},
author = {Jason Cantarella and Al LaPointe and Eric Rawdon},
journal= {arXiv preprint arXiv:1110.3262},
year = {2015}
}
Comments
Summary text file of tight knot lengths and writhing numbers stored in anc/ropelength_data.txt. All other data freely available at http:://www.jasoncantarella.com/ and through Data Conservancy