The Generalized Kauffman-Harary Conjecture is True
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909741828014080 |
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| author | Bakshi, Rhea Palak Guo, Huizheng Montoya-Vega, Gabriel Mukherjee, Sujoy Przytycki, Józef H. |
| author_facet | Bakshi, Rhea Palak Guo, Huizheng Montoya-Vega, Gabriel Mukherjee, Sujoy Przytycki, Józef H. |
| contents | For a reduced alternating diagram of a knot with a prime determinant $p,$ the Kauffman-Harary conjecture states that every non-trivial Fox $p$-coloring of the knot assigns different colors to its arcs. In this paper, we prove a generalization of the conjecture stated nineteen years ago by Asaeda, Przytycki, and Sikora: for every pair of distinct arcs in the reduced alternating diagram of a prime link with determinant $δ,$ there exists a Fox $δ$-coloring that distinguishes them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02645 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Generalized Kauffman-Harary Conjecture is True Bakshi, Rhea Palak Guo, Huizheng Montoya-Vega, Gabriel Mukherjee, Sujoy Przytycki, Józef H. Geometric Topology Primary: 57K10 Secondary: 57M12 For a reduced alternating diagram of a knot with a prime determinant $p,$ the Kauffman-Harary conjecture states that every non-trivial Fox $p$-coloring of the knot assigns different colors to its arcs. In this paper, we prove a generalization of the conjecture stated nineteen years ago by Asaeda, Przytycki, and Sikora: for every pair of distinct arcs in the reduced alternating diagram of a prime link with determinant $δ,$ there exists a Fox $δ$-coloring that distinguishes them. |
| title | The Generalized Kauffman-Harary Conjecture is True |
| topic | Geometric Topology Primary: 57K10 Secondary: 57M12 |
| url | https://arxiv.org/abs/2301.02645 |