Bibliographie
- V. Berthé, M. Rigo,
Introduction, Combinatorics, Automata and Number Theory, V. Berthé, M. Rigo (Eds),
V. Berthé, M. Rigo, Preliminaries (Chapter 1), Combinatorics, Automata and Number Theory, V. Berthé, M. Rigo (Eds),
V. Berthé, A. Siegel, J. Thüswaldner, Substitutions, Rauzy fractals, and tilings (Chapter 5),
Combinatorics, Automata and Number Theory, V. Berthé, M. Rigo (Eds),
Encyclopedia of Mathematics and its Applications 135, © Cambridge University Press (2010).
- V. Berthé
Arithmetic discrete planes are quasicrystals
DGCI 09 LNCS 5810 (2009), 1--12.
- V. Berthé
Discrete geometry and numeration
Actes du colloque "Numération: mathématiques et informatique"
CIRM, 2009.
- Oberwolfach Mini-Workshop: The Pisot Conjecture - From Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets
Report
- V. Berthé, L. Imbert
Diophantine approximation, Ostrowski numeration
and the double-base number system,
Discrete Mathematics & Computer Science,
11 (2009).
- V. Berthé, N. Nakada, R. Natsui
Asymptotic behavior of the number of
solutions for non-Archimedean Diophantine approximations
with restricted denominators
Finite Fields and their Applications 14 (2008), 849--866 .
- P. Arnoux, V. Berthé, Z. Masáková, E. Pelantová
Sturm numbers and substitution invariance of 3iet words
Integers 8 (2008) A14.
- V. Berthé, P. Lecomte, M. Rigo éditeurs
Special issue dedicated to Combinatorics, Automata and Number Theory
Theoret. Comput. Sci. 391 (2008).
- V. Berthé
Discrete geometry and symbolic dynamics
Proceedings of ``The Kiselmanfest: an international symposium
in complex analysis and digital geometry''
Uppsala, Suède, 15--18 mai 2006.
In Mikael Passare (Ed.), Complex Analysis and Digital
Geometry.
Proceedings from the Kiselmanfest, 2006, pp. 81--110.
Acta
Universitatis Upsaliensis, vol. 86. Uppsala: Uppsala University. 364 pp.
ISSN 0502-7454, ISBN 978-91-554-7672-4.
- S. Akiyama, G. Barat, V. Berthé, A. Siegel
Boundary of central tiles
associated with Pisot beta-numeration and purely periodic expansions
Monatshefte für mathematik 155 (2008), 377--419
- V. Berthé, A. Siegel
Purely periodic beta-expansions in the non-unit case
J. Number Theory 127 (2007), 153--172.
- V. Berthé, T. Fernique
Brun expansions, substitutions and discrete geometry
Words 07.
- V. Berthé, C. Frougny, M. Rigo, J. Sakarovitch
On the cost and complexity of the successor function
Words 07.
- V. Berthé, A. de Luca, C. Reutenauer
On an involution of Christoffel words and Sturmian morphisms
European Journal of Combinatorics 29 (2008), 535--553.
- P. Arnoux, V. Berthé, T. Fernique, D. Jamet
Functional stepped surfaces, flips and generalized substitutions
Theoret. Comput. Sci. 380 (2007), 251--267 .
- V. Berthé, B. Nouvel
Discrete rotations and symbolic dynamics
Theoret. Comput. Sci. 380 (2007), 276--285 .
- G. Barat, V. Berthé, P. Liardet, J. Thuswaldner
Dynamical directions
in numeration
Ann. Inst. Fourier (Grenoble) 56 (2006), 1987--2092.
- N. Pytheas Fogg (P. Arnoux, V. Berthé, J. Cassaigne)
Substitutions sur des motifs en
dimension 1
Theoret. Informatics Appl. 41 (2007), 267--284.
- V. Berthé, C. Fiorio, D. Jamet, F. Philippe
On some applications
of generalized functionality for arithmetic discrete planes
Image and Vision Computing 25 (2007), 1671--1684.
- V. Berthé, H. Ei, S. Ito, H. Rao
Invertible susbtitutions and Sturmian words: an application of Rauzy fractals
Theoret. Informatics Appl. 41 (2007), 329--349.
- P. Arnoux, V. Berthé, A. Hilion, A. Siegel
Fractal representation of the attractive lamination of an
automorphism of the free group
Ann. Inst. Fourier (Grenoble) 56 (2006), 2161--2212.
- V. Berthé, A. Siegel
Tilings associated with beta-numeration and
substitution
Integers: electronic journal of combinatorial number theory
5 (2005), A02.
- V. Berthé, B. Nouvel
Density of symbols
in discretized rotation
configurations
Words 2005, 5th International Conference on Words 2005,
Publications du LACIM 36 (2005),163--173.
- P. Arnoux, V. Berthé, D. Jamet
Generalized substitutions and stepped surfaces
Words 2005, 5th International Conference on Words 2005
Publications du LACIM 36 (2005),101--111.
- V. Berthé, M. Rigo
Abstract numeration systems and tilings
MFCS 2005,
30th International Symposium
on Mathematical Foundations of Computer Science
Gdansk, J. Jedrzejowicz, A. Szepietowski Ed., Lect. Notes Comput. Sci. 3618 (2005), 131--143, Springer.
- V. Berthé, N. Nakada, R. Natsui
Arithmetic distributions of convergents arising from Jacobi-Perron
algorithm
Indagationes Mathematicae 17 (2006), 169--185.
- V. Berthé, S. Brlek, P. Choquette
Smooth words over arbitrary alphabets
Theoret. Comput. Sci. 341 (2005), 293--310.
- V. Berthé, S. Ferenczi, L.Q. Zamboni
Interactions between dynamics, arithmetics,
and combinatorics: the good, the bad, and the ugly
Algebraic and Topological Dynamics
S. Kolyada, T. Manin, and T. Ward eds.,
Contemporary Mathematics (CONM), AMS, American Mathematical
Society, 385 (2005), 333--364.
- V. Berthé, M. Rigo
Odometers on regular languages,
Theory Comput. Syst., 40 (2007), 1--31.
- V. Berthé, C. Holton, L.Q. Zamboni
Initial powers of Sturmian words,
Acta Arithmetica, 122 (2006), 315--347.
- V. Berthé, C. Fiorio, D. Jamet
Generalized functionality for arithmetic discrete planes
DGCI 2005, Lecture Notes in Computer Sci. 3429, 276--286,
Springer.
- J.-P. Allouche, V. Berthé
Words in number theory
in Applied Combinatorics on words
N. Lothaire, Cambridge University Press 105 (2005), 520--578.
- V. Berthé, L. Imbert
On Converting Numbers to the Double-Base Number System
Advanced Signal Processing Algorithms, Architecture and Implementations
XIV
Proceedings of SPIE 5559 (2004), 70--78.
- V. Berthé, S. Brlek, P. Choquette
A new characterization of the Fibonacci word
The Eleventh International Conference
on Fibonacci Numbers and Their Applications, July 5--9 2004,
Technical University, Carolo-Wilhelmina, Braunschweig, Allemagne,
Kluwer Academic Publishers, to appear.
- V. Berthé, R. Tijdeman
Lattices and multi-dimensional words
Theoret. Comput. Sci 319 (2004), 177--202.
- P. Arnoux, V. Berthé, A. Siegel
Two-dimensional iterated morphisms and discrete planes
Theoret. Comput. Sci. 319 (2004), 145--176.
- P. Arnoux,V. Berthé, S. Ito
Discrete planes, Z^2-actions, Jacobi-Perron
algorithm and substitutions
Ann. Inst. Fourier (Grenoble)
52 (2002), 1001--1045.
- V. Berthé
Chap. 1: Basic notions (écrit avec A. Siegel)
Chap. 3: Transcendence and automata
Chap. 12: Some open problems
(écrit avec P. Arnoux)
Substitutions in Dynamics, Arithmetics and Combinatorics
édité par V. Berthé, S. Ferenczi, C. Maudit, A. Siegel,
Lecture Notes in Mathematics 1794, Springer Verlag, 2002.
- V. Berthé, R. Tijdeman
Balance properties of
multi-dimensional words
Theoret. Comput. Sci. 273 (2002), 197--224 .
- P. Arnoux,V. Berthé, H. Ei, S. Ito
Tilings, quasicrystals, discrete planes,
generalized substitutions and multidimensional continued fractions
Discrete Mathematics & Theoretical Computer Science,
vol. AA (2001), 59--78 .
- V. Berthé, L. Vuillon
Palindromes and two-dimensional Sturmian sequences
J. Autom. Lang. Comb. 6 (2001), 121--138.
- V. Berthé
Thue-Morse sequence
Encyclopaedia of Mathematics, Supplement II, Kluwer Academic Publishers, 461--462.
- V. Berthé
Autour du système de numération
d'Ostrowski
Bull. Belgian Math. Soc. 8 (2001), 209--239.
- V. Berthé
Sequences of low complexity: automatic
and Sturmian sequencess
``Symbolic dynamics and its applications'' édité par F. Blanchard,
A. Maas, A. Nogueira, LMS, Lecture Note Series 279,
Cambridge University Press (2000), 1--34.
- V. Berthé, H. Nakada
On continued fraction expansions in positive characteristic: equivalence relations
and some metric propertiess
Expositiones Mathematicae 18 (2000), 257--284.
- V. Berthé
Complexité et automates cellulaires linéaires
Theoret. Informatics Appl. 34 (2000), 403--423.
- V. Berthé, L. Vuillon
Suites doubles de basse complexité
Journal
de Théorie des Nombres de Bordeaux 12 (2000), 179--208.
- V. Berthé, L. Vuillon
Tilings and rotations on the torus: a two-dimensional generalization of Sturmian sequences
Discrete Math. 223 (2000), 27--53.
- V. Berthé, N. Chekhova, S. Ferenczi
Covering numbers:
arithmetics and dynamics for rotations and interval exchanges
J. Anal. Math. 79 (1999), 1--31.
- P. Alessandri, V. Berthé
Three distance theorems and combinatorics on words
L'Enseignement Mathématique 44 (1998), 103--132.
- J.-P. Allouche, V. Berthé
Triangle de Pascal, complexité et automates
Bull. Belgian Math. Soc.
4 (1997), 1--23.
- V. Berthé
Fréquences des facteurs des suites sturmiennes
Theoret. Comput. Sci. 165 (1996), 295--309.
- V. Berthé
Entropy in deterministic and random systems
Actes de l'École de Physique Théorique
des Houches: ``Beyond quasicrystals'', Les Éditions de Physique, Springer (1995), 441--463.
- V. Berthé
Combinaisons linéaires de zeta(s)/Pi^s sur F_q(x), pour 1 <= s <= q-2
J. Number Theory 53 (1995), 272--299.
- V. Berthé
Automates et valeurs de
transcendance du logarithme de Carlitz
Acta Arithmetica LXVI.4 (1994), 369--390.
- V. Berthé
Conditional entropy of some automatic sequences
J. Phys. A: Math. Gen. 27 (1994), 7993--8006.
- V. Berthé
Fonction zeta de Carlitz et automates
Journal de Théorie des Nombres de Bordeaux 5 (1993), 53--77.
- V. Berthé
De nouvelles preuves preuves ``automatiques'' de transcendance pour la fonction zeta de Carlitz
Journées Arithmétiques de Genève, Astérisque 209 (1992), 159--168
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Divers
