Sequences, Groups, and Number Theory

Valérie Berthé, Michel Rigo (Herausgeber)

Buch | Softcover

XXVI, 578 Seiten

2019 | 1. Softcover reprint of the original 1st ed. 2018
Springer International Publishing (Verlag)
978-3-030-09874-2 (ISBN)

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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.

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.

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.

Erscheinungsdatum	18.02.2019
Reihe/Serie	Trends in Mathematics
Zusatzinfo	XXVI, 578 p. 87 illus., 15 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	914 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	Amenable groups • Automata • automatic sequences • combinatorics • discrete dynamical systems • Group of automata • Normal numbers • Number Theory • numeration systems • symbolic dynamics • Tilings • Word combinatorics
ISBN-10	3-030-09874-5 / 3030098745
ISBN-13	978-3-030-09874-2 / 9783030098742
Zustand	Neuware