Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/19299
Title: | Novel Structural Properties and An Improved Bound for the Number Distinct Squares in a Strings |
Authors: | Thierry, Adrien |
Advisor: | Deza, Antoine |
Department: | Mathematics |
Keywords: | Combinatorics on Words;free monoid;String Algorithms |
Publication Date: | 2016 |
Abstract: | Combinatorics on words explore words – often called strings in the com- puter science community, or monoids in mathematics – and their structural properties. One of the most studied question deals with repetitions which are a form of redundancy. The thesis focuses on estimating the maximum number of distinct squares in a string of length n. Our approach is to study the combinatorial properties of these overlapping structures, nested systems, and obtain insights into the intricate patterns that squares create. Determin- ing the maximum number of repetitions in a string is of interest in different fields such as biology and computer science. For example, the question arrises when one tries to bound the number of repetitions in a gene or in a computer file to be data compressed. Specific strings containing many repetitions are often of interest for additional combinatorial properties. After a brief review of earlier results and an introduction to the question of bounding the maxi- mum number of distinct squares, we present the combinatorial insights and techniques used to obtain the main result of the thesis: a strengthening of the universal upper bound obtained by Fraenkel and Simpson in 1998. |
URI: | http://hdl.handle.net/11375/19299 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Thierry_Adrien-1179240-Phd_Thesis 2.4.pdf | Thesis | 820.71 kB | Adobe PDF | View/Open |
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