Look Inside Combinatorics, Words and Symbolic Dynamics

Combinatorics, Words and Symbolic Dynamics

Part of Encyclopedia of Mathematics and its Applications

Editors:
Valérie Berthé, Université de Paris VII (Denis Diderot)
Michel Rigo, Université de Liège, Belgium

V. Berthé, M. Rigo, M. de Vries, V. Komornik, B. Rittaud, N. Rampersad, J. Shallit, G. Badkobeh, M. Crochemore, C. S. Iliopoulos, M. Kubica, V. Halava, T. Harju, T. Kärki, M.-P. Béal, D. Perrin, J. Kari, M. Hochman, C. Reutenauer, E. Cesaratto, B. Vallée

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Date Published: March 2016
availability: Available
format: Hardback
isbn: 9781107077027

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Description

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.
- Covers a large scope of topics with a combinatorical flavour and various applications
- Carefully selected authors are specialists in their respective fields
- Serves as an entry point for graduate students, with many pointers to the wider literature
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Product details
- Date Published: March 2016
- format: Hardback
- isbn: 9781107077027
- length: 496 pages
- dimensions: 242 x 163 x 37 mm
- weight: 0.94kg
- contains: 135 b/w illus. 75 exercises
- availability: Available
Table of Contents
List of contributors
Preface
Acknowledgments
1. Preliminaries V. Berthé and M. Rigo
2. Expansions in non-integer bases M. de Vries and V. Komornik
3. Medieties, end-first algorithms, and the case of Rosen continued fractions B. Rittaud
4. Repetitions in words N. Rampersad and J. Shallit
5. Text redundancies G. Badkobeh, M. Crochemore, C. S. Iliopoulos and M. Kubica
6. Similarity relations on words V. Halava, T. Harju and T. Kärki
7. Synchronised automata M.-P. Béal and D. Perrin
8. Cellular automata, tilings and (un)computability J. Kari
9. Multidimensional shifts of finite type and sofic shifts M. Hochman
10. Linearly recursive sequences and Dynkin diagrams C. Reutenauer
11. Pseudo-randomness of a random Kronecker sequence. An instance of dynamical analysis E. Cesaratto and B. Vallée
Notation index
General index.
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Editors
Valérie Berthé, Université de Paris VII (Denis Diderot)
Valérie Berthé is a CNRS Research Director at LIAFA (Laboratoire d'Informatique Algorithmique: Fondements et Applications) at the Université Paris Diderot, Paris 7. She is Deputy Director of the Fondation Sciences Mathématiques de Paris and has authored 70 journal or conference papers. Her main research interests are tilings, numeration systems, substitutive dynamicals systems and symbolic dynamics.
Michel Rigo, Université de Liège, Belgium
Michel Rigo is a full professor in the Department of Mathematics at the Université de Liège, Belgium, and head of the research group in discrete mathematics. He has authored more than 50 journal or conference papers and two books. His main research interests are formal language theory, numeration systems and combinatorics on words.
Contributors
V. Berthé, M. Rigo, M. de Vries, V. Komornik, B. Rittaud, N. Rampersad, J. Shallit, G. Badkobeh, M. Crochemore, C. S. Iliopoulos, M. Kubica, V. Halava, T. Harju, T. Kärki, M.-P. Béal, D. Perrin, J. Kari, M. Hochman, C. Reutenauer, E. Cesaratto, B. Vallée