150 citations · 522 across the 88 of their papers we have counts for
89 papers · 1 filter
Path to homology of Yang-Baxter operators
Jozef H. Przytycki
This paper is an extended version of two talks I gave during workshop ``Loops'13" in Bedlewo in June 2023. In the first talk I gave a historical introduction to Knot Theory. In the…
Kauffman bracket skein module of the connected sum of two solid tori
Rhea Palak Bakshi, Thang T. Q. Lê, Józef H. Przytycki
We determine the structure of the Kauffman bracket skein module of the connected sum of two genus one handlebodies over the ring of Laurent polynomials , ther…
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…
The Montesinos-Nakanishi 3-move conjecture for links up to 20 crossings
Rhea Palak Bakshi, Benjamin A. Burton, Huizheng Guo +4
Yasutaka Nakanishi formulated the following conjecture in 1981: every link is 3-move equivalent to a trivial link. While the conjecture was proved for several specific cases, it re…
Exploring unimodality of the plucking polynomial with delay function
Dionne Ibarra, Alex Landry, Gabriel Montoya-Vega +1
The plucking polynomial is an invariant of rooted trees with connections to knot theory. The polynomial was constructed in 2014 as a tool to analyze lattice crossings after taking…
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,…