Anthony Christiana
YOU?
Author Swipe
View article: Fundamentals of cubic skein modules
Fundamentals of cubic skein modules Open
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 mathematics and physics, including algebraic geometry, hyperboli…
View article: In Search of Homology for Quasigroups of Bol-Moufang Type
In Search of Homology for Quasigroups of Bol-Moufang Type Open
We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define second and third boundary operations, $\partial_2(x,y)$ and…
View article: Chebyshev polynomials and Gram determinants from the Möbius band
Chebyshev polynomials and Gram determinants from the Möbius band Open
This article explores the connection between Chebyshev polynomials and knot theory, specifically in relation to Gram determinants. We reveal intriguing formulae involving the Chebyshev polynomial of the first and second kind. In particular…
View article: Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs
Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs Open
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. Followin…
View article: Psyquandle Coloring Quivers
Psyquandle Coloring Quivers Open
We enhance the psyquandle counting invariant for singular knots and pseudoknots using quivers analogously to quandle coloring quivers. This enables us to extend the in-degree polynomial invariants from quandle coloring quiver theory to the…