New Upper Bounds for Stick Numbers

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.

Publication Details

Journal
ArXiv.org
Published
2025-08-25
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

New Upper Bounds for Stick Numbers

ArXiv.org
Geochemistry and Geologic Mapping
article

New Upper Bounds for Stick Numbers

article en

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.

ArXiv.org
Openalex Percentile: Top 64%
Geochemistry and Geologic Mapping
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New Upper Bounds for Stick Numbers · ArXiv.org (2025) | TGRS Research Map | TGRS