Electronic Theses and Dissertations

Award/Availability

Open Access Thesis

Keywords

Knot theory;

Abstract

The “bridge index” of a knot is the least number of maximal overpasses taken over all diagrams of the knot. A naïve method to determine the bridge index of a knot is to perform Reidemeister moves on diagrams of the knot, and this method quickly becomes tedious to implement by hand. In this paper, we introduce a sequence of Reidemeister moves which we call a “drag the underpass” move and prove how planar diagram codes change as Reidemeister moves are performed. We then use these results to programatically perform Reidemeister moves using Python 2.7 to calculate an upper bound on the bridge index of prime knots with three through twelve crossings. We conclude with discussions of how our results compare to the literature and future work related to these calculations.

Date of Award

2017

Degree Name

Master of Arts

Department

Department of Mathematics

First Advisor

Theron J. Hitchman

Date Original

2017

Object Description

1 PDF file (ix, 112 pages)

Language

EN

File Format

application/pdf

Share

COinS