Combinatorics, Automata and Number Theory

doi:10.1017/CBO9780511777653

This collaborative volume presents trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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List of contributors
pp ix-x
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Preface
pp xi-xviii
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Acknowledgements
pp xix-xx
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1 - Preliminaries
pp 1-33
- By V. Berthé, Université Paris, M. Rigo, Université de Liège
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2 - Number representation and finite automata
pp 34-107
- By CH. Frougny, Université Paris, J. Sakarovitch, France
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3 - Abstract numeration systems
pp 108-162
- By P. Lecomte, Université de Liège, M. Rigo, Université de Liège
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4 - Factor complexity
pp 163-247
- By J. Cassaigne, Institut de mathématiques de Luminy, F. Nicolas, University of Helsinki
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5 - Substitutions, Rauzy fractals and tilings
pp 248-323
- By V. Berthé, Université Paris, A. Siegel, Université Rennes, J. Thuswaldner, University of Leoben
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6 - Combinatorics on Bratteli diagrams and dynamical systems
pp 324-372
- By F. Durand, Université de Picardie Jules Verne
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7 - Infinite words with uniform frequencies, and invariant measures
pp 373-409
- By S. Ferenczi, Université de Picardie Jules Verne, T. Monteil, Université Montpellier
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8 - Transcendence and Diophantine approximation
pp 410-451
- By B. Adamczewski, Université Lyon, Y. Bugeaud, Université de Strasbourg-Mathématiques
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9 - Analysis of digital functions and applications
pp 452-504
- By M. Drmota, Institut für Diskrete Mathematik, P. J. Grabner, Institut für Analysis
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10 - The equality problem for purely substitutive words
pp 505-529
- By J. Honkala, University of Turku
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11 - Long products of matrices
pp 530-562
- By V. D. Blondel, Université catholique de Louvain, R. M. Jungers, Université catholique de Louvain
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References
pp 563-593
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Notation index
pp 594-598
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General index
pp 599-615
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Combinatorics, Automata and Number Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

List of contributors
pp ix-x

Preface
pp xi-xviii

Acknowledgements
pp xix-xx

1 - Preliminaries
pp 1-33

2 - Number representation and finite automata
pp 34-107

3 - Abstract numeration systems
pp 108-162

4 - Factor complexity
pp 163-247

5 - Substitutions, Rauzy fractals and tilings
pp 248-323

6 - Combinatorics on Bratteli diagrams and dynamical systems
pp 324-372

7 - Infinite words with uniform frequencies, and invariant measures
pp 373-409

8 - Transcendence and Diophantine approximation
pp 410-451

9 - Analysis of digital functions and applications
pp 452-504

10 - The equality problem for purely substitutive words
pp 505-529

11 - Long products of matrices
pp 530-562

References
pp 563-593

Notation index
pp 594-598

General index
pp 599-615

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Combinatorics, Automata and Number Theory

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