Date of Award

2010

Document Type

Dissertation/Thesis

Submission Date

October 2026

Abstract

Famous mathematician Paul Erdèos conjectured the existence of infinite sequences of symbols where no two adjacent subsequences are permutations of one another. It can easily be checked that no such sequence can be constructed using only three symbols, but as few as four symbols are sufficient. Here, we expand this concept to include sequences that may contain 'do not know'' characters, called holes. These holes make the undesired subsequences more common. We explore both finite and infinite sequences. For infinite sequences, we use iterating morphisms to construct the non-repetitive sequences with either a finite number of holes or infinitely many holes. We also discuss the problem of using the minimum number of different symbols.

Comments

by William Severa.

Extent

viii, 39 p. : ill. (some col.)

Identifier

779617841

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