4 papers · 1 filter
Fundamentals of cubic skein modules
Rhea Palak Bakshi, Anthony Christiana, Huizheng Guo +6
Over the past thirty-seven years, the study of linear and quadratic skein modules has produced a rich and far-reaching skein theory, intricately connected to diverse areas of mathe…
Chebyshev polynomials and Gram determinants from the Möbius band
Anthony Christiana, Dionne Ibarra, Gabriel Montoya-Vega
This article explores the connection between Chebyshev polynomials and knot theory, specifically in relation to Gram determinants. We reveal intriguing formulae involving the Cheby…
Low Dimensional Homology of the Yang-Baxter Operators Yielding the HOMFLYPT Polynomial
Anthony Christiana, Ben Clingenpeel, Huizheng Guo +4
In this paper, we analyze the homology of the Yang-Baxter Operators yielding the HOMFLYPT polynomial, reducing the computation of the -th homology of for arb…
Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs
Anthony Christiana, Huizheng Guo, Jozef H. Przytycki
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 . In doing so,…