An infinite family of knots whose hexagonal mosaic number is only realized in non-reduced projections
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866908971312349184 |
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| author | Howards, Hugh Li, Jiong Liu, Xiaotian Paulec, Anna |
| author_facet | Howards, Hugh Li, Jiong Liu, Xiaotian Paulec, Anna |
| contents | We give an infinite family of knots such that for any given $r \geq 3$, the family contains a knot which can be embedded on a hexagonal $r$-mosaic, but cannot fit on a hexagonal $r$-mosaic in an embedding that achieves its crossing number. This extends the rectangular mosaic result of Ludwig, Evans, and Paat. We also introduce a new tool for systematically finding all possible flypes for the diagram of any link thus making it easier to find all possible minimal crossing embeddings of prime, alternating knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_03697 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | An infinite family of knots whose hexagonal mosaic number is only realized in non-reduced projections Howards, Hugh Li, Jiong Liu, Xiaotian Paulec, Anna Geometric Topology Quantum Algebra 57M25 We give an infinite family of knots such that for any given $r \geq 3$, the family contains a knot which can be embedded on a hexagonal $r$-mosaic, but cannot fit on a hexagonal $r$-mosaic in an embedding that achieves its crossing number. This extends the rectangular mosaic result of Ludwig, Evans, and Paat. We also introduce a new tool for systematically finding all possible flypes for the diagram of any link thus making it easier to find all possible minimal crossing embeddings of prime, alternating knots. |
| title | An infinite family of knots whose hexagonal mosaic number is only realized in non-reduced projections |
| topic | Geometric Topology Quantum Algebra 57M25 |
| url | https://arxiv.org/abs/1912.03697 |