Publications
- V. Berthé, H. Goulet-Ouellet,
Obstructions to return preservation for episturmian morphisms
- V. Berthé, H. Goulet-Ouellet, C.-F. Nyberg
Brodda, D. Perrin and K. Petersen,
Density of group languages in shift spaces
- V. Berthé, T. Karimov, J. Ouaknine, M. Vahanwala,
J. Worrell
The Monadic Theory of Toric Words
- V. Berthé, C. Reutenauer
On the three distance theorem
The Mathematical Intelligencer, to appear. PDF
- V. Berthé, A. Mimouni
Recurrence and Frequencies
WORDS 2023, LNCS 13899, pp. 11-13, 2023 DOI.
- V. Berthé, H. Goulet-Ouellet
On substitutions preserving their return sets
WORDS 2023, LNCS 13899, 2023 DOI.
- V. Berthé, R. Yassawi
Meyer sets, Pisot numbers, and self-similarity in symbolic dynamical systems
Documents mathématiques, Société Mathématique de France, to appear.
- V. Berthé, W. Steiner, J. Thuswaldner
Multidimensional continued fractions and symbolic codings of toral translations
Journal of the European Mathematical Society (JEMS), 25(12) (2023), 4997-5057 DOI.
- V. Berthé, J.-W. Lee
Dynamics of Ostrowski skew-product: I. Limit laws and Hausdorff dimensions
Trans. Amer. Math. Soc, 376 (2023), 7947-7982 DOI.
- V. Berthé, K. Dajani, C. Kalle, E. Krawczyk, H. Kuru, A. Thevis
Rational approximations, multidimensional continued fractions and lattice reduction
.
``Women in Numbers Europe 4-Research Directions in Number Theory'', Springer's AWM series, to appear.
- V. Berthé, S. Puzynina
On the rigidity of Arnoux-Rauzy words
- M.-P. Béal, V. Berthé, D. Perrin, A. Restivo
A note on one-sided recognizable morphisms
- V. Berthé, E. Cesaratto, P. Rotondo, M. D. Safe
Lochs-type theorems beyond positive entropy
Monatsh. Math. 200 (2023), no. 4, 737-779 DOI.
- V. Berthé, P. Cecchi Bernales, R. Yassawi
Coboundaries and eigenvalues of finitary S-adic systems
- V. Berthé, H. Nakada, R. Natsui, B. Vallée
Analysis of generalized continued fraction algorithms over polynomials
Finite Fields and Their Applications, 73 (2021), 101849.
- V. Berthé
On decision problems for substitutions in symbolic dynamics
RP20, Reachability problems, Lecture Notes in Computer Science 12448, Springer 2020, 3-19.
- V. Berthé, E. Cesaratto, F. Paccaut, P. Rotondo, M. D. Safe, B. Vallée
Two arithmetical sources and their associated tries
AofA 2020, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms.
- V. Berthé, P. Cecchi Bernales, F. Durand, J. Leroy, D. Perrin, S.Petite
On the dimension group of unimodular S-adic subshifts
Monatshefte für Mathematik 194 (2021) 687-217.
- V. Berthé, W. Steiner, J. Thuswaldner
On the second Lyapunov exponent of some multidimensional continued fraction algorithms
Mathematics of computation 90 (2021) 883-905.
- V. Berthé, C. Frougny, M. Rigo, J. Sakarovitch
The carry propagation of the successor function
Advances in Applied Mathematics 120: 102062 (2020).
- V. Berthé, W. Steiner, J. Thuswaldner
Geometry, dynamics, and arithmetic of S-adic shifts
Annales de l'Institut Fourier 69 (2019), 1347-1409.
- V. Berthé
Symbolic dynamics and representations
Cours donné lors des Journées Nationales de Calcul Formel, CIRM, 2017.
- V. Berthé, P. Cecchi Bernales
Balancedness and coboundaries in symbolic systems
Theoret. Comput. Sci. 777 (2019), 93-110.
- V. Berthé, D. H. Kim
Some constructions for the higher-dimensional three-distance theorem
Acta Arithmetica 184 (2018), 385-411.
- V. Berthé, F. Dolce, F. Durand, J. Leroy, D. Perrin
Rigidity and substitutive dendric words
Internat. J. Found. Comput. Sci. 29 (2018), 705-720.
- V. Berthé, W. Steiner, J. Thuswaldner, R. Yassawi
Recognizability for sequences of morphisms
Ergodic Theory & Dynam. Sys. 39 (2019), 2896-2931.
- V. Berthé, M. Rigo, Preliminaries (Chapter 1)
Sequences, groups and number theory, V. Berthé, M. Rigo (Eds)
Birkhäauser, Trends in Mathematics, Springer, 2018.
- V. Berthé, L. Lhote, B. Vallée,
The Brun Gcd Algorithm in high dimensions is almost always subtractive.
Journal of Symbolic Computation 85 (2018), 72-107.
- V. Berthé, C. De Felice, V. Delecroix, F. Dolce, J. Leroy, D. Perrin, C. Reutenauer, G. Rindone
Specular sets
Theoret. Comput. Sci. 684 (2017), 3--28.
- V. Berthé, Th. Fernique, M. Sablik
Effective S-adic symbolic dynamical systems
CiE 2016, LNCS 9709 (2016) 13-23.
- V. Berthé, L. Lhote, B. Vallée,
Analysis of the Brun Gcd Algorithm
ISSAC 2016, ACM 2016, 87-94.
- V. Berthé,
S-adic expansions related to continued fractions
RIMS Kyokuroku Bessatsu, B58 (2016), 61-84.
- V. Berthé, M. Rigo, Preliminaries (Chapter 1)
Combinatorics, Words and Symbolic dynamics, V. Berthé, M. Rigo (Eds),
Encyclopedia of Mathematics and its Applications 159, Cambridge University Press (2016).
- V. Berthé, C. De Felice, V. Delecroix, F. Dolce, J. Leroy, D. Perrin, C. Reutenauer, G. Rindone
Specular sets
Words 2015, LNCS 9304, Springer (2015), 210--222.
- V. Berthé, L. Lhote, B. Vallée,
A probabilistic analysis of the plain multiple gcd algorithm.
Journal of Symbolic Computation 74 (2016) 425--474.
- V. Berthé, V. Delecroix, F. Dolce, D. Perrin, C. Reutenauer, G. Rindone
Return words of linear involutions and fundamental groups.
Ergodic Theory Dynam. Systems 37 (2017) 693--715.
- V. Berthé, E. Cesaratto, P. Rotondo, B. Vallée, A. Viola
Recurrence function on Sturmian words: a probabilistic study.
MFCS (2015), LNCS 9234 (2015) 116--128.
- V. Berthé, M. Minervino, W. Steiner, J. Thuswaldner
The S-adic Pisot conjecture on two letters.
Top. and its Appl., 205 (2016), 47-57.
.
- S. Akiyama, M. Barge, V. Berthé, J.-Y. Lee and A. Siegel
On the Pisot substitution conjecture
Mathematics of Aperiodic Order, J. Kellendonk, D. Lenz, J. Savinien (Eds)
Progress in Mathematics (Birkhäuser), Vol. 309 (2015) 33--72.
- V. Berthé, C. De Felice, F. Dolce, J. Leroy, D. Perrin, C. Reutenauer, G. Rindone
Acyclic, connected and tree sets
Monatsh. Math. 176 (2015) 521-550.
- V. Berthé, C. De Felice, F. Dolce, J. Leroy, D. Perrin, C. Reutenauer, G. Rindone
Maximal bifix decoding
Discrete Math. 338 (2015) 725-742.
- V. Berthé, J. Bourdon, T. Jolivet, A. Siegel
A combinatorial approach to products of Pisot substitutions
Ergodic Theory Dynam. Systems 36 (2016), 1757-1794.
- V. Berthé, S. Labbé
Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-PoincarÉ Algorithm
Advances in Applied Mathematics 63 (2015) 90-130.
- V. Berthé, C. De Felice, F. Dolce, J. Leroy, D. Perrin, C. Reutenauer, G. Rindone
Bifix codes and interval exchanges
Journal of Pure and Applied Algebra 219 (2015) 2781-2798.
- V. Berthé, C. De Felice, F. Dolce, J. Leroy, D. Perrin, C. Reutenauer, G. Rindone
The finite index basis property
Journal of Pure and Applied Algebra 219 (2015) 2521-2537.
- V. Berthé, H. Nakada, R. Natsui, B. Vallée
Fine costs for the Euclid algorithm on polynomials and Farey maps
Advances in Applied Mathematics 54 (2014) 27-65.
- V. Berthé, T. Jolivet, A. Siegel
Connectedness of fractals associated with Arnoux-Rauzy substitutions
RAIRO-Theoretical Informatics and Applications 48 (2014) 249-266.
- V. Berthé, V. Delecroix
Beyond substitutive dynamical systems: S-adic expansions
RIMS Lecture note `Kokyuroku Bessatu' B46 (2014) 81-123.
- V. Berthé, J. Bourdon, T. Jolivet, A. Siegel
Generating discrete planes with substitutions
Words 2013, LNCS 8079 (2013) 107-118.
- V. Berthé, S. Labbé
Convergence and Factor Complexity for the Arnoux-Rauzy-Poincaré Algorithm
Words 2013, LNCS 8079 (2013) 71-82.
- V. Berthé, D. Jamet, T. Jolivet, X. Provençal
Critical connectedness of thin arithmetical discrete planes
DGCI 2013, LNCS 7749, 107-118. Long version
- V. Berthé, J. Creusefond, L. Lhote, B. Vallée
Multiple GCDs. Probabilistic analysis of the plain algorithm
ISSAC 2013, ACM, 37-44.
- V. Berthé, E. Domenjoud, D. Jamet, X. Provençal
Fully Subtractive Algorithm, Tribonacci numeration and connectedness of
discrete planes
RIMS Lecture note `Kokyuroku Bessatu' B46 (2014) 159-174.
- V. Berthé, J. Shallit éditeurs
Special Issue in Honor of the 60th Birthday of Jean-Paul Allouche
Journal of Integer Sequences, Vol. 16, 2013, Issue 2.
- V. Berthé J. Cassaigne, W. Steiner
Balance properties of Arnoux-Rauzy words
International Journal of Algebra and Computation IJAC 23 (2013) 689-704.
- V. Berthé, T. Jolivet, A. Siegel
Substitutive Arnoux-Rauzy sequences have pure discrete spectrum
Uniform distribution theory 7 (2012) 173-197.
- V. Berthé, A. Lacasse, G. Paquin, X. Provençal
A study of Jacobi-Perron boundary words for the generation of discrete planes
Theoret. Comput. Sci. 502 (2013) 118-142.
- V. Berthé, D. Frettlöh, V. Sirvent
Selfdual substitutions in dimension one
European Journal of Combinatorics 33 (2012) 981-1000.
- V. Berthé,
Numeration and discrete dynamical systems
Computing, 94 (2012) 369-387.
DOI
- V. Berthé, S. Labbé,
Uniformly balanced words with linear complexity and prescribed letter frequencies
WORDS 2011, Electronic Proceedings in Theoretical Computer Science 63.
- V. Berthé
Multidimensional Euclidean algorithms, numeration and substitutions
Integers 11B (2011) A2.
- V. Berthé
About thin arithmetic discrete planes
Theoret. Comput. Sci., 412 (2011) 4757-4769.
DOI
- V. Berthé, S. Labbé,
An Arithmetic and Combinatorial Approach to three-dimensional Discrete Lines
DGCI 2011, Lecture Notes in Computer Science 6607 Springer (2011) 47-58.
- V. Berthé, T. Fernique
Brun expansions of stepped surfaces
Discrete Mathematics, 311 (2011) 521-543.
DOI
- V. Berthé, A. Siegel, P. Surer, W. Steiner, J. Thuswaldner,
Fractal tiles associated with shift radix systems
Advances in Mathematics 226 (2011) 139-175.
DOI
- Oberwolfach Mini-Workshop: Combinatorics on words
Report
- 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. Thuswaldner, 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.
Acta
Universitatis Upsaliensis, vol. 86. Uppsala: Uppsala University. pp. 81-110.
- 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
Proceedings of the Eleventh International Conference on Fibonacci Numbers and their Applications,
Congressus Numerantium 194 (2009) 67-76.
- 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
Astérisque 209 (1992), 159-168.
Divers
