Combinatorics, Automata and Number Theory (Encyclopedia of Mathematics and its Applications, Series Number 135)

This collaborative volume presents recent 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.

Valérie Berthé is 'Directeur de Recherche CNRS' in the Montpellier Laboratory of Informatics, Robotics, and Micro-electronics (LIRMM) at the University of Montpellier 2, France.

Michel Rigo is a Professor in the Department of Mathematics at the University of Liège, Belgium.