Date of Award

5-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Timothy B. Flowers, Ph.D.

Second Advisor

Rick Adkins, Ph.D.

Third Advisor

Francisco E. Alarcón, Ph.D.

Abstract

In 1960, Paul Erdös proposed the following question: what is the minimum number of characters needed to construct an infinitely long sequence without repetition, where repetition is defined as having two adjacent segments which are permutations of each other [6]. Erdös provided proof that this is not possible using three characters. In 1970, P.A.B. Pleasants proved it is possible with 5 characters [7], leaving the question of whether it is possible with four characters open until in 1992, when Veikko Keränen found such a sequence [9]. Keränen continues to research methods of finding such strings. While repetition is a basic concept understood by children, analysis of non-repetitive sequences is known to require extensive computation. The purpose of this thesis is to develop a tool to assist in the study of non-repetitive and strongly non-repetitive sequences. The tool uses a matrix developed from a complete vocabulary of prime segments.

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