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Avoiding abelian squares in infinite partial words

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Date Issued:
2010
Summary:
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.
Title: Avoiding abelian squares in infinite partial words.
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Name(s): Severa, William.
Harriet L. Wilkes Honors College
Type of Resource: text
Genre: Thesis
Issuance: multipart monograph
Date Issued: 2010
Publisher: Florida Atlantic University
Physical Form: electronic resource
Extent: viii, 39 p. : ill. (some col.)
Language(s): English
Summary: 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.
Identifier: 779617841 (oclc), 3335460 (digitool), FADT3335460 (IID), fau:1416 (fedora)
Note(s): by William Severa.
Thesis (B.A.)--Florida Atlantic University, Honors College, 2010.
Includes bibliography.
Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.
Subject(s): Abelian groups
Mathematics -- Study and teaching (Higher)
Combinatorial analysis
Combinatorial set theory
Probabilities
Held by: FBoU FAUER
Persistent Link to This Record: http://purl.flvc.org/FAU/3335460
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Host Institution: FAU

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