Marnie Phipps

Publication Date

12-1999

Advisor(s) - Committee Chair

Claus Ernst, Lyn Miller, Mark Robinson

Comments

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Degree Program

Department of Mathematics

Degree Type

Master of Science

Abstract

The cubic lattice is a graph in R3 whose vertices are all points with coordinates (x, y, z) where x, y, and z are integers and whose edges are of unit length where they are line segments connecting the vertices. This thesis addresses how many edges of the cubic lattice are needed to realize a given knot or link. The main theorem proves that a four crossing link, denoted 4 2/I, needs a minimum of 28 edges. In addition the number of edges needed to realize a family of knot, called (p, 2) torus knots, is given.

Disciplines

Mathematics | Physical Sciences and Mathematics

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