5 citations · 8 across the 14 of their papers we have counts for
14 papers
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…
Temperley-Lieb Categories on Non-Orientable Surfaces
Dionne Ibarra, Gabriel Montoya-Vega, Benjamin Morris
In this paper we present the construction of a skeletal diagram category, which we call the square with bands category. This category extends the Temperley-Lieb (TL) category, wher…
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…
A robot that unknots knots
Connie On Yu Hui, Dionne Ibarra, Louis H. Kauffman +4
Consider a robot that remembers only the starting position and walks along a knot once on a knot diagram, switching every undercrossing it meets until it returns to the starting po…
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…
On the notion of Khovanov A-adequacy
Lizzie Buchanan, Huizheng Guo, Gabriel Montoya-Vega +2
The concept of adequate links, introduced by Lickorish and Thistlethwaite as a generalization of alternating links, has recently gained interest among knot theorists in the context…
Alexander-Conway and Bracket Polynomials of Pretzel Links
Alan Hernandez-Flores, Gabriel Montoya-Vega
Polynomial invariants constitute a dynamic and essential area of study in the mathematical theory of knots. From the pioneer Alexander polynomial, the revolutionary Jones polynomia…
Independence complexes of circle graphs
Rhea Palak Bakshi, Ali Guo, Dionne Ibarra +4
Independence complexes of circle graphs are purely combinatorial objects. However, when constructed from some diagram of a link , they reveal topological properties of , more…
A Study of Gram Determinants in Knot Theory
Dionne Ibarra, Gabriel Montoya-Vega
Historically originated as a sub-field of topology, knot theory is an active area of mathematical investigation that has strong connections with a diverse set of scientific fields…
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…
A Glimpse of the Khovanov Homology of T(2,n) Via Long Exact Sequence
Gabriel Montoya-Vega
Khovanov homology is a powerful link invariant: a categorification of the Jones polynomial that enjoys a rich and beautiful algebraic structure. This homology theory has been exten…
On a new Gram determinant from the Möbius band
Dionne Ibarra, Gabriel Montoya-Vega
Gram determinants earned traction among knot theorists after E. Witten's presumption about the existence of a 3-manifold invariant connected to the Jones polynomial. Triggered by t…
The Generalized Kauffman-Harary Conjecture is True
Rhea Palak Bakshi, Huizheng Guo, Gabriel Montoya-Vega +2
For a reduced alternating diagram of a knot with a prime determinant the Kauffman-Harary conjecture states that every non-trivial Fox -coloring of the knot assigns differen…
On framings of links in 3-manifolds
Rhea Palak Bakshi, Dionne Ibarra, Gabriel Montoya-Vega +2
We show that the only way of changing the framing of a link by ambient isotopy in an oriented -manifold is when the manifold has a properly embedded non-separating . This c…