Constructions of and Bounds on the Toric Mosaic Number
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908628762492928 |
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| author | Heiney, Kendall Kipe, Margaret Pezzimenti, Samantha Pontes, Kaelyn Ta, Luc |
| author_facet | Heiney, Kendall Kipe, Margaret Pezzimenti, Samantha Pontes, Kaelyn Ta, Luc |
| contents | Knot mosaics were introduced by Kauffman and Lomonaco in the context of quantum knots, but have since been studied for their own right. A classical knot mosaic is formed on a square grid. In this work, we identify opposite edges of the square to form mosaics on the surface of a torus. We provide two algorithms for efficiently constructing toric mosaics of torus knots, providing upper bounds for the toric mosaic number. Using these results and a computer search, we provide a census of known toric mosaic numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructions of and Bounds on the Toric Mosaic Number Heiney, Kendall Kipe, Margaret Pezzimenti, Samantha Pontes, Kaelyn Ta, Luc Geometric Topology 57K10 Knot mosaics were introduced by Kauffman and Lomonaco in the context of quantum knots, but have since been studied for their own right. A classical knot mosaic is formed on a square grid. In this work, we identify opposite edges of the square to form mosaics on the surface of a torus. We provide two algorithms for efficiently constructing toric mosaics of torus knots, providing upper bounds for the toric mosaic number. Using these results and a computer search, we provide a census of known toric mosaic numbers. |
| title | Constructions of and Bounds on the Toric Mosaic Number |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2504.02265 |