Combinatorics, automata and number theory

edited by Valérie Berthé, Michel Rigo

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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[目次]

  • Introduction Valerie Berthe and Michel Rigo
  • 1. Preliminaries
  • 2. Number representation and finite automata Ch. Frougny and J. Sakarovitch
  • 3. Abstract numeration systems P. Lecomte and M. Rigo
  • 4. Factor complexity J. Cassaigne and F. Nicolas
  • 5. Substitutions, Rauzy fractals, and tilings V. Berthe, A. Siegel and J. Thuswaldner
  • 6. Combinatorics on Bratelli diagrams and dynamical systems F. Durand
  • 7. Infinite words with uniform frequencies, and invariant measures S. Ferenczi and T. Monteil
  • 8. Transcendence and Diophantine approximation B. Adamczewski and Y. Bugeaud
  • 9. Analysis of digital functions and applications M. Drmota and P. Grabner
  • 10. The equality problem for purely substitutive words J. Honkala
  • 11. Long products of matrices V. Blondel and R. Jungers
  • References
  • Notation index
  • General index.

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この本の情報

書名 Combinatorics, automata and number theory
著作者等 Berthé, V.
Rigo, Michel
Berthe Valerie
シリーズ名 Encyclopedia of mathematics and its applications
出版元 Cambridge University Press
刊行年月 2010
ページ数 xix, 615 p.
大きさ 25 cm
ISBN 9780521515979
NCID BB02972048
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言語 英語
出版国 イギリス
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