Year: 2025
Type: article
Abstract: Sangyop Lee has done much work to determine the knot types of twisted torus knots, including classifying the twisted torus knots which are the unknot. Among the unknotted twisted torus knots are those of the form [Formula: see text], where [Formula: see text] is the ith Fibonacci number. Here, we consider twisted torus knots with parameters that are defined recursively, similarly to the Fibonacci sequence. We call these Horadam parameters, after the generalization of the Fibonacci sequence introduced by Horadam. Here, we provide families of twisted torus knots that generalize Lee’s work with Horadam parameters. Additionally, we provide lists of primitive/primitive and primitive/Seifert twisted torus knots and connect these lists to the Horadam twisted torus knots.
Author: Brandy Doleshal
Institution: Sam Houston State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416398069