New Upper Bounds for Stick Numbers

Fuente: arXiv
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Bibliographic Details
Main Authors: Cantarella, Jason, Rechnitzer, Andrew, Schumacher, Henrik, Shonkwiler, Clayton
Format: Preprint
Published: 2025
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author Cantarella, Jason
Rechnitzer, Andrew
Schumacher, Henrik
Shonkwiler, Clayton
author_facet Cantarella, Jason
Rechnitzer, Andrew
Schumacher, Henrik
Shonkwiler, Clayton
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_18263
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle New Upper Bounds for Stick Numbers
Cantarella, Jason
Rechnitzer, Andrew
Schumacher, Henrik
Shonkwiler, Clayton
Geometric Topology
57K10
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.
title New Upper Bounds for Stick Numbers
topic Geometric Topology
57K10
url https://arxiv.org/abs/2508.18263