Overview

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.

Full Product Details

Author:   Valérie Berthé (Université de Paris VII (Denis Diderot)) ,  Michel Rigo (Université de Liège, Belgium)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Volume:   159
Dimensions:   Width: 16.30cm , Height: 3.70cm , Length: 24.20cm
Weight:   0.940kg
ISBN:  

9781107077027

ISBN 10:   1107077028
Pages:   496
Publication Date:   26 February 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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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Author Information

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 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.

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