Formal Languages, Automata and Numeration Systems 1 Introduction to Combinatorics on Words
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          | Main Author | |
|---|---|
| Format | eBook | 
| Language | English | 
| Published | 
        Newark
          John Wiley & Sons, Incorporated
    
        2014
     | 
| Edition | 1 | 
| Subjects | |
| Online Access | Get full text | 
Cover
| Author | Rigo, Michel | 
    
|---|---|
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| Publisher | John Wiley & Sons, Incorporated | 
    
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| SubjectTerms | Computer programming Formal languages Machine theory  | 
    
| Subtitle | Introduction to Combinatorics on Words | 
    
| TableOfContents | 3.6. Other combinatorial complexity measures -- 3.6.1. Abelian complexity -- 3.6.2. k-Abelian complexity -- 3.6.3. k-Binomial complexity -- 3.6.4. Arithmetical complexity -- 3.6.5. Pattern complexity -- 3.7. Bibliographic notes and comments -- Bibliography -- Index -- Volume 2 - Contents -- Volume 2 - Index Cover page -- Half-Title page -- Title page -- Copyright page -- Contents -- Foreword -- Introduction -- I.1. What this book is or is not about -- I.2. A few words about what you will find -- I.3. How to read this book -- I.4. Acknowledgments -- 1: Words and Sequences from Scratch -- 1.1. Mathematical background and notation -- 1.1.1. About asymptotics -- 1.1.2. Algebraic number theory -- 1.2. Structures, words and languages -- 1.2.1. Distance and topology -- 1.2.2. Formal series -- 1.2.3. Language, factor and frequency -- 1.2.4. Period and factor complexity -- 1.3. Examples of infinite words -- 1.3.1. About cellular automata -- 1.3.2. Links with symbolic dynamical systems -- 1.3.3. Shift and orbit closure -- 1.3.4. First encounter with β-expansions -- 1.3.5. Continued fractions -- 1.3.6. Direct product, block coding and exercises -- 1.4. Bibliographic notes and comments -- 2: Morphic Words -- 2.1. Formal definitions -- 2.2. Parikh vectors and matrices associated with a morphism -- 2.2.1. The matrix associated with a morphism -- 2.2.2. The tribonacci word -- 2.3. Constant-length morphisms -- 2.3.1. Closure properties -- 2.3.2. Kernel of a sequence -- 2.3.3. Connections with cellular automata -- 2.4. Primitive morphisms -- 2.4.1. Asymptotic behavior -- 2.4.2. Frequencies and occurrences of factors -- 2.5. Arbitrary morphisms -- 2.5.1. Irreducible matrices -- 2.5.2. Cyclic structure of irreducible matrices -- 2.5.3. Proof of theorem 2.35 -- 2.6. Factor complexity and Sturmian words -- 2.7. Exercises -- 2.8. Bibliographic notes and comments -- 3: More Material on Infinite Words -- 3.1. Getting rid of erasing morphisms -- 3.2. Recurrence -- 3.3. More examples of infinite words -- 3.4. Factor Graphs and special factors -- 3.4.1. de Bruijn graphs -- 3.4.2. Rauzy graphs -- 3.5. From the Thue-Morse word to pattern avoidance  | 
    
| Title | Formal Languages, Automata and Numeration Systems 1 | 
    
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