عنوان

Sequences, Groups, and Number Theory /

331969152X

9783319691527

3319691511

9783319691510

Sequences, Groups, and Number Theory /

[Book]

Valérie Berthé, Michel Rigo, editors.

Cham :

Birkhäuser,

2018.

1 online resource

Trends in mathematics

Intro; Preface; Chapter 2 by Michael Coons and Lukas Spiegelhofer Number Theoretic Aspects of Regular Sequences; Chapter 3 by Émilie CharlierFirst-Order Logic and Numeration Systems; Chapter 4 by Jason BellSome Applications of Algebra to Automatic Sequences; Chapter 5 by Pascal Ochem, Michaël Rao, and Matthieu RosenfeldAvoiding or Limiting Regularities in Words; Chapter 6 by Caïus Wojcik and Luca ZamboniColoring Problems for Infinite Words; Chapter 7 by Verónica Becher and Olivier CartonNormal Numbers and Computer Science; Chapter 8 by Manfred MadritschNormal Numbers and Symbolic Dynamics.

1.5.2 Formal Series1.5.3 Codes; 1.5.4 Automata; 1.6 Sequences and Machines; 1.6.1 Automatic Sequences; 1.6.2 Regular Sequences; 1.7 Dynamical Systems; 1.7.1 Topological Dynamical Systems; 1.7.2 Measure-Theoretic Dynamical Systems; 1.7.3 Symbolic Dynamics; 2 Number Theoretic Aspects of Regular Sequences; 2.1 Introduction; 2.1.1 Two Important Questions; 2.1.2 Three (or Four) Hierarchies in One; 2.2 From Automatic to Regular to Mahler; 2.2.1 Definitions; 2.2.2 Some Comparisons Between Regular and Mahler Functions; 2.3 Size and Growth; 2.3.1 Lower Bounds; 2.3.2 Upper Bounds.

2.3.3 Maximum Values and the Finiteness Property2.4 Analytic and Algebraic Properties of Mahler Functions; 2.4.1 Analytic Properties of Mahler Functions; 2.4.2 Rational-Transcendental Dichotomy of Mahler Functions; 2.5 Rational-Transcendental Dichotomy of Regular Numbers; 2.6 Diophantine Properties of Mahler Functions; 2.6.1 Rational Approximation of Mahler Functions; 2.6.2 A Transcendence Test for Mahler Functions; 2.6.3 Algebraic Approximation of Mahler Functions; 3 First-Order Logic and Numeration Systems; 3.1 Introduction; 3.2 Recognizable Sets of Nonnegative Integers.

3.2.1 Unary Representations3.2.2 Integer Bases; 3.2.3 Positional Numeration Systems; 3.2.4 Abstract Numeration Systems; 3.2.5 The Cobham-Semenov Theorem; 3.3 First-Order Logic and b-Automatic Sequences; 3.3.1 b-Definable Sets of Integers; 3.3.2 The Büchi-Bruyère Theorem; 3.3.3 The First-Order Theory of ""426830A N,+,Vb""526930B Is Decidable; 3.3.4 Applications to Decidability Questions for b-Automatic Sequences; 3.4 Enumeration; 3.4.1 b-Regular Sequences; 3.4.2 N-Recognizable and N∞-RecognizableFormal Series; 3.4.3 Counting b-Definable Properties of b-Automatic Sequences Is b-Regular

Chapter 9 by Nathalie Aubrun, Sebastián Barbieri, and Emmanuel JeandelAbout the Domino Problem for Subshifts on GroupsChapter 10 by Ines Klimann and Matthieu Picantin Automaton (Semi)groups: Wang Tilings and Schreier Tries; Chapter 11 by Laurent BartholdiAmenability Groups and G-Sets; Acknowledgments; Contents; Contributors; 1 General Framework; 1.1 Conventions; 1.2 Algebraic Structures; 1.3 Words; 1.3.1 Finite Words; 1.3.2 Infinite Words; 1.3.3 Number Representations; 1.3.4 Normality; 1.3.5 Repetitions in Words; 1.4 Morphisms; 1.5 Languages and Machines; 1.5.1 Languages of Finite Words.

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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.--

Springer Nature

com.springer.onix.9783319691527

Sequences, Groups, and Number Theory.

9783319691510

Number theory.

Combinatorics & graph theory.

Discrete mathematics.

Groups & group theory.

MATHEMATICS-- Algebra-- Intermediate.

Number theory.

Number theory.

MAT-- 002040

Berthé, Valérie

Rigo, Michel

20200823102644.0

pn

[Book]

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