New Upper Bounds for Stick Numbers
Fuente:
arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912553396862976 |
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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 |