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Combinatorics, Automata and Number Theory

Part of Encyclopedia of Mathematics and its Applications

Valérie Berthé, Michel Rigo, Ch. Frougny, J. Sakarovitch, P. Lecomte, J. Cassaigne, F. Nicolas, A. Siegel, J. Thuswaldner, F. Durand, S. Ferenczi, T. Monteil, B. Adamczewski, Y. Bugeaud, M. Drmota, P. Grabner, J. Honkala, V. Blondel, R. Jungers
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  • Date Published: August 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521515979

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About the Authors
  • 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.

    • Provides a useful overview of the most recent results
    • Written for readers with either a mathematical or computer science background
    • Chapters are self-contained so readers do not have to consult extra material
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    Product details

    • Date Published: August 2010
    • format: Hardback
    • isbn: 9780521515979
    • length: 636 pages
    • dimensions: 236 x 160 x 43 mm
    • weight: 1.06kg
    • contains: 60 b/w illus. 150 exercises
    • availability: Available
  • Table of Contents

    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.

  • Editors

    Valérie Berthé, Université de Paris VII
    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, Université de Liège, Belgium
    Michel Rigo is a Professor in the Department of Mathematics at the University of Liège, Belgium.

    Contributors

    Valérie Berthé, Michel Rigo, Ch. Frougny, J. Sakarovitch, P. Lecomte, J. Cassaigne, F. Nicolas, A. Siegel, J. Thuswaldner, F. Durand, S. Ferenczi, T. Monteil, B. Adamczewski, Y. Bugeaud, M. Drmota, P. Grabner, J. Honkala, V. Blondel, R. Jungers

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