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Topics In Random Knots And R-Matrices From Frobenius Algebras, Enver Karadayi
Topics In Random Knots And R-Matrices From Frobenius Algebras, Enver Karadayi
USF Tampa Graduate Theses and Dissertations
In this dissertation, we study two areas of interest in knot theory: Random knots in the unit cube, and the Yang-Baxter solutions constructed from Frobenius algebras.
The study of random knots can be thought of as a model of DNA strings situated in confinement. A random knot with n vertices is a polygonal loop formed by selecting n distinct points in the unit cube, for a positive integer n, and connecting these points by straight line segments successively, such that the last point selected is joined with the first one. We present a step by step description of our algorithm …