Sequences, Groups, and Number Theory

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.

List of contents

General Framework.- Number Theoretic Aspects of Regular Sequences.- First-order Logic and Numeration System.- Some Applications of Algebra to Automatic Sequences.- Avoiding or Limiting Regularities in Words.- Coloring Problems for Infinite Words.- Normal Numbers and Computer Science.- Normal Numbers and Symbolic Dynamics.- About the Domino Problem for Subshifts on Groups.- Automation (Semi)Groups: Wang Tilings and Schreier Tries.- Amenability of Groups and G-Sets.- Index.- References.

About the author

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.

Summary

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

Product details

• Assisted by: Valéri Berthé (Editor), Valérie Berthé (Editor), Rigo (Editor), Rigo (Editor), Michel Rigo (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2019
• EAN: 9783030098742
• ISBN: 978-3-0-3009874-2
• No. of pages: 578
• Dimensions: 156 mm x 236 mm x 33 mm
• Weight: 914 g
• Illustrations: XXVI, 578 p. 87 illus., 15 illus. in color.
• Series: Trends in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; Zahlentheorie, B, Gruppen und Gruppentheorie, Mathematik für Informatiker, Group Theory, Combinatorics, Mathematics and Statistics, Discrete Mathematics in Computer Science, Discrete Mathematics, Number Theory, Groups & group theory, Group Theory and Generalizations, Computer science—Mathematics, Maths for computer scientists, tilings