Dissertations and Theses @ UNI
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.
Year of Submission
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)
Copyright
©2017 Genevieve R. Johnson
Language
en
File Format
application/pdf
Recommended Citation
Johnson, Genevieve R., "The programmatic manipulation of planar diagram codes to find an upper bound on the bridge index of prime knots" (2017). Dissertations and Theses @ UNI. 462.
https://scholarworks.uni.edu/etd/462
