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. 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. Preliminaries / V. Berthé, M. Rigo -- Number Representation And Finite Automata / Ch. Frougny, J. Sakarovitch -- Abstract Numeration Systems / P. Lecomte, M. Rigo -- Factor Complexity / J. Cassaigne, F. Nicolas -- Substitutions, Rauzy Fractals And Tilings / V. Berthé, A. Siegel, J. Thuswaldner -- Combinatorics On Bratteli Diagrams And Dynamical Systems / F. Durand -- Infinite Words With Uniform Frequencies, And Invariant Measures / S. Ferenczi, T. Monteil -- Transcendence And Diophantine Approximation / B. Adamczewski, Y. Bugeaud -- Analysis Of Digital Functions And Applications / M. Drmota, P.j. Grabner -- The Equality Problem For Purely Substitutive Words / J. Honkala -- Long Products Of Matrices / V.d. Blondel, R.m. Jungers. Edited By Valérie Berthé, Michel Rigo. Includes Bibliographical References And Indexes.