© 2018

Sequences, Groups, and Number Theory

  • Valérie Berthé
  • Michel Rigo


  • 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 Trends in Mathematics book series (TM)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Valérie Berthé, Michel Rigo
    Pages 1-36
  3. Michael Coons, Lukas Spiegelhofer
    Pages 37-87
  4. Émilie Charlier
    Pages 89-141
  5. Pascal Ochem, Michaël Rao, Matthieu Rosenfeld
    Pages 177-212
  6. Caïus Wojcik, Luca Q. Zamboni
    Pages 213-231
  7. Verónica Becher, Olivier Carton
    Pages 233-269
  8. Manfred Madritsch
    Pages 271-329
  9. Nathalie Aubrun, Sebastián Barbieri, Emmanuel Jeandel
    Pages 331-389
  10. Ines Klimann, Matthieu Picantin
    Pages 391-431
  11. 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.


Combinatorics Word combinatorics Normal numbers Automata Group of automata Discrete dynamical systems normal numbers amenable groups number theory numeration systems automatic sequences symbolic dynamics tilings

Editors and affiliations

  • Valérie Berthé
    • 1
  • Michel Rigo
    • 2
  1. 1.IRIF, Université Paris DiderotParisFrance
  2. 2.Department of MathematicsUniversity of LiègeLiègeBelgium

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