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Combinatorics, Words and Symbolic Dynamics
About this book
Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.
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Information
Table of contents
- Cover
- Half-title
- Series information
- Title page
- Copyright information
- Table of contents
- List of contributors
- Preface
- Acknowledgments
- 1 Preliminaries
- 2 Expansions in non-integer bases
- 3 Medieties, end-first algorithms, and the case of Rosen continued fractions
- 4 Repetitions in words
- 5 Text redundancies
- 6 Similarity relations on words
- 7 Synchronised automata
- 8 Cellular automata, tilings and (un)computability
- 9 Multidimensional shifts of finite type and sofic shifts
- 10 Linearly recursive sequences and Dynkin diagrams
- 11 Pseudo-randomness of a random Kronecker sequence. An instance of dynamical analysis
- Bibliography
- Notation index
- General index