10 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…
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…
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…