# Algorithmic Combinatorics on Partial Words

CRC Press, Nov 19, 2007 - Mathematics - 392 pages
The discrete mathematics and theoretical computer science communities have recently witnessed explosive growth in the area of algorithmic combinatorics on words. The next generation of research on combinatorics of partial words promises to have a substantial impact on molecular biology, nanotechnology, data communication, and DNA computing. Delving into this emerging research area, Algorithmic Combinatorics on Partial Words presents a mathematical treatment of combinatorics on partial words designed around algorithms and explores up-and-coming techniques for solving partial word problems as well as the future direction of research.

This five-part book begins with a section on basics that covers terminology, the compatibility of partial words, and combinatorial properties of words. The book then focuses on three important concepts of periodicity on partial words: period, weak period, and local period. The next part describes a linear time algorithm to test primitivity on partial words and extends the results on unbordered words to unbordered partial words while the following section introduces some important properties of pcodes, details a variety of ways of defining and analyzing pcodes, and shows that the pcode property is decidable using two different techniques. In the final part, the author solves various equations on partial words, presents binary and ternary correlations, and covers unavoidable sets of partial words.

Setting the tone for future research in this field, this book lucidly develops the central ideas and results of combinatorics on partial words.

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### Contents

 List of Figures 9 Preface 13 BASICS 23 Preliminaries on Partial Words 25 Combinatorial Properties of Partial Words 43 PERIODICITY 61 Fine and Wilf s Theorem 63 Critical Factorization Theorem 93
 CODING 223 Pcodes of Partial Words 225 Deciding the Pcode Property 257 FURTHER TOPICS 279 Equations on Partial Words 281 Correlations of Partial Words 297 Unavoidable Sets of Partial Words 325 Solutions to Selected Exercises 345

 Guibas and Odlyzkos Theorem 117 PRIMITIVITY 155 Primitive Partial Words 157 Unbordered Partial Words 199