Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917935385149440 |
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| author | Christiana, Anthony Guo, Huizheng Przytycki, Jozef H. |
| author_facet | Christiana, Anthony Guo, Huizheng Przytycki, Jozef H. |
| contents | In this paper we compute the Reduced Fox Coloring Group of the diagrams of Wheel Graphs which can also be represented at the closure of the braids $(σ_1 σ_2^{-1})^n$. In doing so, we utilize Fibonacci numbers and their properties.
Following this, we generalize our result to compute the Alexander-Burau-Fox Module over the ring $\mathbb{Z}[t^{\pm 1}]$ for the same class of links. In our computation, Chebyshev polynomials function as a generalization of Fibonacci Numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19979 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs Christiana, Anthony Guo, Huizheng Przytycki, Jozef H. Geometric Topology Number Theory Primary: 57K10 Secondary: 57M12, 11B39 In this paper we compute the Reduced Fox Coloring Group of the diagrams of Wheel Graphs which can also be represented at the closure of the braids $(σ_1 σ_2^{-1})^n$. In doing so, we utilize Fibonacci numbers and their properties. Following this, we generalize our result to compute the Alexander-Burau-Fox Module over the ring $\mathbb{Z}[t^{\pm 1}]$ for the same class of links. In our computation, Chebyshev polynomials function as a generalization of Fibonacci Numbers. |
| title | Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs |
| topic | Geometric Topology Number Theory Primary: 57K10 Secondary: 57M12, 11B39 |
| url | https://arxiv.org/abs/2310.19979 |