Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs

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 \((\sigma_1 \sigma_2^{-1})^n\). In doing so, we utilize Fibonacci numbers and their properties. Following this, we generalize our result to compute the A...

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Bibliographic Details
Published inarXiv.org
Main Authors Anthony, Christiana, Guo, Huizheng, Przytycki, Jozef H
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.10.2023
Subjects
Chebyshev approximation
Coloring
Fibonacci numbers
Graphical representations
Graphs
Group theory
Modules
Polynomials
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Summary: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 \((\sigma_1 \sigma_2^{-1})^n\). 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.
ISSN:2331-8422