2 - Pattern Matching

Summary

The chapter is mostly about combinatorics on words, an important topic since many algorithms are based on combinatorial properties of their input. Several problems are related to periodicity in words, which is a major combinatorial tool in many algorithms presented in following chapters. The stringologic proof of Fermat’s little theorem, codicity testing, distinct periodic words, and problems about conjugate words are introductory problems in applications of periodicities. Then a couple of problems related to famous abstract words: Fibonacci, Thue-Morse and Oldenburger- Kolakoski sequences are presented. They are followed by some algorithmic constructions of certain special supersequences and superwords as well of interesting classes of words: Skolem and Langford sequences. Many problems in this chapters are of algorithmic and constructive type.