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  • © 2018

Sequences, Groups, and Number Theory

Birkhäuser
  • Discusses new research areas and results for sequences and number theory
  • Analyzes the relationship of sequence and group theory to theory of computation and applications of computer science
  • Describes combinatorics on words with a variety of theoretical approaches

Part of the book series: Trends in Mathematics (TM)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxvi
  2. General Framework

    • Valérie Berthé, Michel Rigo
    Pages 1-36
  3. Number Theoretic Aspects of Regular Sequences

    • Michael Coons, Lukas Spiegelhofer
    Pages 37-87
  4. First-Order Logic and Numeration Systems

    • Émilie Charlier
    Pages 89-141
  5. Avoiding or Limiting Regularities in Words

    • Pascal Ochem, Michaël Rao, Matthieu Rosenfeld
    Pages 177-212
  6. Coloring Problems for Infinite Words

    • Caïus Wojcik, Luca Q. Zamboni
    Pages 213-231
  7. Normal Numbers and Computer Science

    • Verónica Becher, Olivier Carton
    Pages 233-269
  8. Normal Numbers and Symbolic Dynamics

    • Manfred Madritsch
    Pages 271-329
  9. About the Domino Problem for Subshifts on Groups

    • Nathalie Aubrun, Sebastián Barbieri, Emmanuel Jeandel
    Pages 331-389
  10. Automaton (Semi)groups: Wang Tilings and Schreier Tries

    • Ines Klimann, Matthieu Picantin
    Pages 391-431
  11. Amenability of Groups and G-Sets

    • Laurent Bartholdi
    Pages 433-544
  12. Back Matter

    Pages 545-576

About this book

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. 


This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Editors and Affiliations

  • IRIF, Université Paris Diderot, Paris, France

    Valérie Berthé

  • Department of Mathematics, University of Liège, Liège, Belgium

    Michel Rigo

About the editors

Valérie Berthé is a researcher at the Institut de Recherche en Informatique Fondamentale, which is a joint project between the Centre National del Recherche Scientifique and the University Paris-Diderot. 

Michel Rigo is a professor in the Unité de Mathématiques Discrétes at the Université de Liége.

Bibliographic Information

Buy it now

Buying options

eBook USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access