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Avoiding abelian squares in infinite partial words
 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 nonrepetitive 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 nonrepetitive 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 

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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 nonprofit 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 