Combinatorics, Words and Symbolic Dynamics

Surveys trends arising from the applications and interactions between combinatorics, symbolic dynamics and theoretical computer science.

Valérie Berthé (Edited by), Michel Rigo (Edited by)

9781107077027, Cambridge University Press

Hardback, published 26 February 2016

496 pages, 135 b/w illus. 75 exercises
24.2 x 16.3 x 3.7 cm, 0.94 kg

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.

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.

Subject Areas: Computer science [UY], Complex analysis, complex variables [PBKD], Discrete mathematics [PBD], Mathematics [PB]