Combinatorics, Automata and Number Theory

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Cambridge University Press, Aug 12, 2010 - Mathematics - 615 pages
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This collaborative volume presents recent 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

Number representation and finite automata
34
Abstract numeration systems
108
Factor complexity
163
Substitutions Rauzy fractals and tilings
248
Combinatorics on Bratteli diagrams and dynamical systems
324
Infinite words with uniform frequencies
373
Transcendence and Diophantine approximation
410
Analysis of digital functions and applications
452
The equality problem for purely substitutive words
505
Long products of matrices
530
References
563
Notation index
594
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About the author (2010)

Valerie Berthe is `Directeur de Recherches CNRS' In the `Laboratoired' Informatique Algorithmique: Fondements et Applications' (LIAFA) at the University Paris Diderot-Paris 7, France.
Michel Rigo is a Professor in the Department of Mathematics at the University of Liege, Belgium.

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