Combinatorics, Automata and Number Theory

This collaborative volume presents trends arising from the fruitful interaction between combinatorics on words, automata and number theory.

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

9780521515979, Cambridge University Press

Hardback, published 12 August 2010

636 pages, 60 b/w illus. 150 exercises
23.6 x 16 x 4.3 cm, 1.08 kg

This collaborative volume presents trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.

Introduction Valérie Berthé and Michel Rigo
1. Preliminaries
2. Number representation and finite automata Ch. Frougny and J. Sakarovitch
3. Abstract numeration systems P. Lecomte and M. Rigo
4. Factor complexity J. Cassaigne and F. Nicolas
5. Substitutions, Rauzy fractals, and tilings V. Berthé, A. Siegel and J. Thuswaldner
6. Combinatorics on Bratelli diagrams and dynamical systems F. Durand
7. Infinite words with uniform frequencies, and invariant measures S. Ferenczi and T. Monteil
8. Transcendence and Diophantine approximation B. Adamczewski and Y. Bugeaud
9. Analysis of digital functions and applications M. Drmota and P. Grabner
10. The equality problem for purely substitutive words J. Honkala
11. Long products of matrices V. Blondel and R. Jungers
References
Notation index
General index.

Subject Areas: Mathematical theory of computation [UYA], Number theory [PBH], Discrete mathematics [PBD]