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Berthé, Valérie

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Author ID: berthe.valerie Recent zbMATH articles by "Berthé, Valérie"
Published as: Berthé, Valérie; Berthé, V.; Berthé, Valerie; Berthe, Valerie; Berthe, Valérie
Homepage: https://www.irif.fr/~berthe/
External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr
Member of Collectives: Fogg, N. Pytheas; Lothaire, M.
Documents Indexed: 105 Publications since 1992, including 5 Books
Reviewing Activity: 87 Reviews
all top 5

Co-Authors

18 single-authored
13 Siegel, Anne
9 Perrin, Dominique
9 Rigo, Michel
8 Dolce, Francesco
8 Leroy, Julien
8 Reutenauer, Christophe
7 Rindone, Giuseppina
7 Thuswaldner, Jörg Maximilian
7 Vallée, Brigitte
6 Arnoux, Pierre
6 Steiner, Wolfgang
5 De Felice, Clelia
5 Jolivet, Timo
5 Nakada, Hitoshi
4 Delecroix, Vincent
4 Jamet, Damien
4 Labbé, Sébastien
4 Lhote, Loïck
4 Natsui, Rie
3 Ferenczi, Sébastien
3 Fernique, Thomas
3 Ito, Shunji
3 Provençal, Xavier
3 Vuillon, Laurent
2 Akiyama, Shigeki
2 Barat, Guy
2 Bourdon, Jérémie
2 Brlek, Srečko
2 Cecchi Bernales, Paulina
2 Choquette, Philippe
2 Durand, Fabien
2 Ei, Hiromi
2 Shallit, Jeffrey O.
2 Tijdeman, Robert
2 Zamboni, Luca Quardo
1 Alessandri, Pascal
1 Allouche, Jean-Paul Simon
1 Barge, Marcy M.
1 Besse, Philippe C.
1 Beukers, Frits
1 Bryyère, Véronique
1 Cassaigne, Julien
1 Cesaratto, Eda
1 Chekhova, Nataliya
1 Clark, Alex
1 Creusefond, Jean
1 Damanik, David
1 de Luca, Aldo
1 Dehornoy, Patrick
1 Domenjoud, Eric
1 Felice, Clelia
1 Fiorio, Christophe
1 Fogg, N. Pytheas
1 Fokkink, Robbert Johan
1 Frettlöh, Dirk
1 Frougny, Christiane
1 Hilion, Arnaud
1 Holton, Charles G.
1 Imbert, Laurent
1 Karhumaki, Juhani
1 Kim, Donghan
1 Kraaikamp, Cor
1 Lacasse, Annie
1 Lebœuf, Patricio
1 Lecomte, Pierre B. A.
1 Lee, Jeong-Yup
1 Lenz, Daniel H.
1 Liardet, Pierre
1 Masáková, Zuzana
1 Massot, Marc
1 Mauduit, Christian
1 Métivier, Guy
1 Minervino, Milton
1 Nouvel, Bertrand
1 Nowotka, Dirk
1 Paquin, Geneviève
1 Patras, Frédéric
1 Pelantová, Edita
1 Petite, Samuel
1 Rao, Hui
1 Rotondo, Pablo
1 Sablik, Mathieu
1 Sakarovitch, Jacques
1 Sirvent, Víctor F.
1 Surer, Paul
1 Viola, Alfredo
1 Yassawi, Reem

Publications by Year

Citations contained in zbMATH Open

83 Publications have been cited 1,031 times in 628 Documents Cited by Year
Substitutions in dynamics, arithmetics and combinatorics. Zbl 1014.11015
Fogg, N. Pytheas (ed.); Berthé, Valérie (ed.); Ferenczi, Sébastien (ed.); Mauduit, Christian (ed.); Siegel, A. (ed.)
263
2002
Tilings and rotations on the torus: A two-dimensional generalization of Sturmian sequences. Zbl 0970.68124
Berthé, Valérie; Vuillon, Laurent
44
2000
Three distance theorems and combinatorics on words. Zbl 0997.11051
Alessandri, Pascal; Berthé, Valérie
43
1998
Tilings associated with beta-numeration and substitutions. Zbl 1139.37008
Berthé, Valérie; Siegel, Anne
32
2005
Initial powers of Sturmian sequences. Zbl 1117.37005
Berthé, Valérie; Holton, Charles; Zamboni, Luca Q.
30
2006
Dynamical directions in numeration. Zbl 1138.37005
Barat, Guy; Berthé, Valérie; Liardet, Pierre; Thuswaldner, Jörg
29
2006
On an involution of Christoffel words and Sturmian morphisms. Zbl 1213.68476
Berthé, Valérie; de Luca, Aldo; Reutenauer, Christophe
29
2008
Frequencies of factors of Sturmian sequences. (Fréquences des facteurs des suites sturmiennes.) Zbl 0872.11018
Berthé, Valérie
26
1996
On the Pisot substitution conjecture. Zbl 1376.37043
Akiyama, S.; Barge, M.; Berthé, V.; Lee, J.-Y.; Siegel, A.
26
2015
Beyond substitutive dynamical systems: \(S\)-adic expansions. Zbl 1376.37033
Berthé, Valérie; Delecroix, Vincent
26
2014
Combinatorics, automata, and number theory. Zbl 1197.68006
Berthé, Valérie (ed.); Rigo, Michel (ed.)
23
2010
On continued fraction expansions in positive characteristic: equivalence relations and some metric properties. Zbl 1024.11050
Berthé, Valérie; Nakada, Hitoshi
22
2000
Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions. Zbl 1017.11006
Arnoux, Pierre; Berthé, Valérie; Ito, Shunji
21
2002
Interactions between dynamics, arithmetics and combinatorics: the good, the bad, and the ugly. Zbl 1156.37301
Berthé, Valérie; Ferenczi, Sébastien; Zamboni, Luca Q.
17
2005
Balance properties of multi-dimensional words. Zbl 0997.68091
Berthé, Valérie; Tijdeman, Robert
16
2002
Acyclic, connected and tree sets. Zbl 1309.68160
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
16
2015
Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions. Zbl 1190.11005
Akiyama, Shigeki; Barat, Guy; Berthé, Valérie; Siegel, Anne
15
2008
Palindromes and two-dimensional Sturmian sequences. Zbl 1002.11026
Berthé, Valérie; Vuillon, Laurent
15
2001
Tilings, quasicrystals, discrete planes, generalized substitutions, and multidimensional continued fractions. Zbl 1017.68147
Arnoux, Pierre; Berthé, Valérie; Ei, Hiromi; Ito, Shunji
14
2001
Maximal bifix decoding. Zbl 1309.68159
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
14
2015
On substitution invariant Sturmian words: an application of Rauzy fractals. Zbl 1140.11014
Berthé, Valérie; Ei, Hiromi; Ito, Shunji; Rao, Hui
13
2007
Substitutions, Rauzy fractals and tilings. Zbl 1247.37015
Berthé, Valérie; Siegel, Anne; Thuswaldner, Jörg
12
2010
Functional stepped surfaces, flips, and generalized substitutions. Zbl 1119.68136
Arnoux, Pierre; Berthé, Valérie; Fernique, Thomas; Jamet, Damien
12
2007
Factor complexity of \(S\)-adic words generated by the Arnoux-Rauzy-Poincaré algorithm. Zbl 1310.68170
Berthé, V.; Labbé, S.
12
2015
Two-dimensional iterated morphisms and discrete planes. Zbl 1068.37004
Arnoux, Pierre; Berthé, Valérie; Siegel, Anne
12
2004
Bifix codes and interval exchanges. Zbl 1357.68152
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
11
2015
On the numeration system of Ostrowski. (Autour dy système de numération d’Ostrowski.) Zbl 0994.68100
Berthé, Valérie
11
2001
Purely periodic \(\beta \)-expansions in the Pisot non-unit case. Zbl 1197.11139
Berthé, Valerie; Siegel, Anne
11
2007
Sequences of low complexity: Automatic and Sturmian sequences. Zbl 0976.11014
Berthé, Valérie
10
2000
The finite index basis property. Zbl 1357.68115
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
10
2015
Double sequences of low complexity. (Suites doubles de basse complexité.) Zbl 1018.37010
Berthé, Valérie; Vuillon, Laurent
9
2000
Fractal representation of the attractive lamination of an automorphism of the free group. Zbl 1146.20020
Arnoux, Pierre; Berthé, Valérie; Hilion, Arnaud; Siegel, Anne
9
2006
Pascal’s triangle, complexity and automata. (Triangle de Pascal, complexité et automates.) Zbl 0922.11012
Allouche, Jean-Paul; Berthé, Valérie
9
1997
Brun expansions of stepped surfaces. Zbl 1236.11011
Berthé, Valérie; Fernique, Thomas
8
2011
Fractal tiles associated with shift radix systems. Zbl 1221.11018
Berthé, Valérie; Siegel, Anne; Steiner, Wolfgang; Surer, Paul; Thuswaldner, Jörg M.
8
2011
Multidimensional Euclidean algorithms, numeration and substitutions. Zbl 1273.11014
Berthé, Valerie
7
2011
Geometry, dynamics, and arithmetic of \(S\)-adic shifts. (Géométrie, dynamique, et arithmétique des décalages \(S\)-adiques.) Zbl 1433.37010
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M.
7
2019
Recognizability for sequences of morphisms. Zbl 07114239
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M.; Yassawi, Reem
7
2019
A combinatorial approach to products of Pisot substitutions. Zbl 1378.37036
Berthé, Valérie; Bourdon, Jérémie; Jolivet, Timo; Siegel, Anne
6
2016
Lattices and multi-dimensional words. Zbl 1068.37005
Berthé, Valérie; Tijdeman, Robert
6
2004
Smooth words over arbitrary alphabets. Zbl 1077.68082
Berthé, Valérie; Brlek, Srečko; Choquette, Philippe
5
2005
Substitutive Arnoux-Rauzy sequences have pure discrete spectrum. Zbl 1313.37004
Berthé, Valérie; Jolivet, Timo; Siegel, Anne
5
2012
Balance properties of Arnoux-Rauzy words. Zbl 1269.68073
Berthé, Valérie; Cassaigne, Julien; Steiner, Wolfgang
5
2013
An arithmetic and combinatorial approach to three-dimensional discrete lines. Zbl 1272.52019
Berthé, Valérie; Labbé, Sébastien
5
2011
Abstract numeration systems and tilings. Zbl 1156.68443
Berthé, Valérie; Rigo, Michel
5
2005
Sturm numbers and substitution invariance of 3iet words. Zbl 1202.11021
Arnoux, Pierre; Berthé, Valérie; Masáková, Zuzana; Pelantová, Edita
5
2008
Covering numbers: Arithmetics and dynamics for rotations and interval exchanges. Zbl 0996.37006
Berthé, Valérie; Chekhova, Nataliya; Ferenczi, Sébastien
5
1999
Probabilistic analyses of the plain multiple gcd algorithm. Zbl 1346.68308
Berthé, Valérie; Lhote, Loïck; Vallée, Brigitte
5
2016
Generating discrete planes with substitutions. Zbl 1400.11075
Berthé, Valérie; Bourdon, Jérémie; Jolivet, Timo; Siegel, Anne
4
2013
Rigidity and substitutive dendric words. Zbl 1448.68365
Berthé, V.; Dolce, F.; Durand, F.; Leroy, J.; Perrin, D.
4
2018
Diophantine approximation, Ostrowski numeration and the double-base number system. Zbl 1221.11017
Berthé, Valérie; Imbert, Laurent
4
2009
Critical connectedness of thin arithmetical discrete planes. Zbl 1382.68246
Berthé, Valérie; Jamet, Damien; Jolivet, Timo; Provençal, Xavier
4
2013
Complexity and linear cellular automata. (Complexité et automates cellulaires linéaires.) Zbl 0988.68116
Berthé, Valérie
4
2000
Odometers on regular languages. Zbl 1107.68046
Berthé, Valérie; Rigo, Michel
4
2007
Carlitz \(\zeta\)-function and automata. (Fonction \(\zeta\) de Carlitz et automates.) Zbl 0784.11025
Berthé, Valérie
3
1993
Conditional entropy of some automatic sequences. Zbl 0846.11019
Berthé, Valérie
3
1994
Specular sets. Zbl 1330.68231
Berthé, Valérie; Felice, Clelia; Delecroix, Vincent; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
3
2015
Connectedness of fractals associated with Arnoux-Rauzy substitutions. Zbl 1326.37007
Berthé, Valérie; Jolivet, Timo; Siegel, Anne
3
2014
Sequences, groups, and number theory. Zbl 1394.05002
Berthé, Valérie (ed.); Rigo, Michel (ed.)
3
2018
Return words of linear involutions and fundamental groups. Zbl 1375.37033
Berthé, Valérie; Delecroix, Vincent; Dolce, Francesco; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
3
2017
Uniformly balanced words with linear complexity and prescribed letter frequencies. Zbl 1331.68161
Berthé, Valérie; Labbé, Sébastien
3
2011
Automates et valeurs de transcendance du logarithme de Carlitz. (Automata and transcendental values of the Carlitz logarithm). Zbl 0784.11024
Berthé, Valérie
3
1994
Balancedness and coboundaries in symbolic systems. Zbl 1423.68366
Berthé, Valérie; Cecchi Bernales, Paulina
3
2019
Linear combinations of \(\zeta(s)/ \Pi^ s\) over \(F_ q(x)\) for \(1\leq s\leq q-2\). (Combinaisons linéaires de \(\zeta(s)/ \Pi^ s\) sur \(F_ q(x)\), pour \(1\leq s\leq q-2\).) Zbl 0853.11062
Berthé, Valérie
2
1995
New “automatic” proofs for the transcendence of the Carlitz zeta function. (De nouvelles preuves “automatiques” de transcendance pour la fonction zeta de Carlitz.) Zbl 0788.11020
Berthé, Valérie
2
1992
Combinatorics, words and symbolic dynamics. Zbl 1370.05003
Berthé, Valérie (ed.); Rigo, Michel (ed.)
2
2016
Specular sets. Zbl 1383.68066
Berthé, Valérie; De Felice, Clelia; Delecroix, Vincent; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
2
2017
The Brun gcd algorithm in high dimensions is almost always subtractive. Zbl 1427.11143
Berthé, Valérie; Lhote, Loïck; Vallée, Brigitte
2
2018
Fine costs for Euclid’s algorithm on polynomials and Farey maps. Zbl 1285.11102
Berthé, Valérie; Nakada, Hitoshi; Natsui, Rie; Vallée, Brigitte
2
2014
The \(S\)-adic Pisot conjecture on two letters. Zbl 1368.37020
Berthé, Valérie; Minervino, Milton; Steiner, Wolfgang; Thuswaldner, Jörg
2
2016
Arithmetic discrete planes are quasicrystals. Zbl 1261.52013
Berthé, Valérie
2
2009
Fully subtractive algorithm, Tribonacci numeration and connectedness of discrete planes. Zbl 1352.11013
Berthé, Valérie; Domenjoud, Éric; Jamet, Damien; Provençal, Xavier
2
2014
Entropy in deterministic and random systems. Zbl 0884.28014
Berthé, V.
1
1995
\(S\)-adic expansions related to continued fractions. Zbl 1372.37024
Berthé, Valérie
1
2016
Convergence and factor complexity for the Arnoux-Rauzy-Poincaré algorithm. Zbl 1400.11018
Berthé, Valérie; Labbé, Sebastien
1
2013
Analysis of the Brun GCD algorithm. Zbl 1364.11162
Berthé, Valérie; Lhote, Loïck; Vallée, Brigitte
1
2016
Preliminaries [to: Combinatorics, words and symbolic dynamics]. Zbl 1404.11003
Berthé, Valérie; Rigo, Michel
1
2016
Discrete geometry and symbolic dynamics. Zbl 1204.37011
Berthé, Valérie
1
2009
Discrete rotations and symbolic dynamics. Zbl 1115.68119
Berthé, Valérie; Nouvel, Bertrand
1
2007
Selfdual substitutions in dimension one. Zbl 1252.68164
Berthé, Valérie; Frettlöh, Dirk; Sirvent, Victor
1
2012
Multiple GCDs. Probabilistic analysis of the plain algorithm. Zbl 1360.68972
Berthé, Valérie; Creusefond, Jean; Lhote, Loïck; Vallée, Brigitte
1
2013
On the second Lyapunov exponent of some multidimensional continued fraction algorithms. Zbl 07298459
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M.
1
2021
On the dimension group of unimodular \(\mathcal{S}\)-adic subshifts. Zbl 07328633
Berthé, Valérie; Cecchi Bernales, P.; Durand, Fabien; Leroy, Julien; Perrin, Dominique; Petite, S.
1
2021
On the second Lyapunov exponent of some multidimensional continued fraction algorithms. Zbl 07298459
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M.
1
2021
On the dimension group of unimodular \(\mathcal{S}\)-adic subshifts. Zbl 07328633
Berthé, Valérie; Cecchi Bernales, P.; Durand, Fabien; Leroy, Julien; Perrin, Dominique; Petite, S.
1
2021
Geometry, dynamics, and arithmetic of \(S\)-adic shifts. (Géométrie, dynamique, et arithmétique des décalages \(S\)-adiques.) Zbl 1433.37010
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M.
7
2019
Recognizability for sequences of morphisms. Zbl 07114239
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M.; Yassawi, Reem
7
2019
Balancedness and coboundaries in symbolic systems. Zbl 1423.68366
Berthé, Valérie; Cecchi Bernales, Paulina
3
2019
Rigidity and substitutive dendric words. Zbl 1448.68365
Berthé, V.; Dolce, F.; Durand, F.; Leroy, J.; Perrin, D.
4
2018
Sequences, groups, and number theory. Zbl 1394.05002
Berthé, Valérie; Rigo, Michel
3
2018
The Brun gcd algorithm in high dimensions is almost always subtractive. Zbl 1427.11143
Berthé, Valérie; Lhote, Loïck; Vallée, Brigitte
2
2018
Return words of linear involutions and fundamental groups. Zbl 1375.37033
Berthé, Valérie; Delecroix, Vincent; Dolce, Francesco; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
3
2017
Specular sets. Zbl 1383.68066
Berthé, Valérie; De Felice, Clelia; Delecroix, Vincent; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
2
2017
A combinatorial approach to products of Pisot substitutions. Zbl 1378.37036
Berthé, Valérie; Bourdon, Jérémie; Jolivet, Timo; Siegel, Anne
6
2016
Probabilistic analyses of the plain multiple gcd algorithm. Zbl 1346.68308
Berthé, Valérie; Lhote, Loïck; Vallée, Brigitte
5
2016
Combinatorics, words and symbolic dynamics. Zbl 1370.05003
Berthé, Valérie; Rigo, Michel
2
2016
The \(S\)-adic Pisot conjecture on two letters. Zbl 1368.37020
Berthé, Valérie; Minervino, Milton; Steiner, Wolfgang; Thuswaldner, Jörg
2
2016
\(S\)-adic expansions related to continued fractions. Zbl 1372.37024
Berthé, Valérie
1
2016
Analysis of the Brun GCD algorithm. Zbl 1364.11162
Berthé, Valérie; Lhote, Loïck; Vallée, Brigitte
1
2016
Preliminaries [to: Combinatorics, words and symbolic dynamics]. Zbl 1404.11003
Berthé, Valérie; Rigo, Michel
1
2016
On the Pisot substitution conjecture. Zbl 1376.37043
Akiyama, S.; Barge, M.; Berthé, V.; Lee, J.-Y.; Siegel, A.
26
2015
Acyclic, connected and tree sets. Zbl 1309.68160
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
16
2015
Maximal bifix decoding. Zbl 1309.68159
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
14
2015
Factor complexity of \(S\)-adic words generated by the Arnoux-Rauzy-Poincaré algorithm. Zbl 1310.68170
Berthé, V.; Labbé, S.
12
2015
Bifix codes and interval exchanges. Zbl 1357.68152
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
11
2015
The finite index basis property. Zbl 1357.68115
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
10
2015
Specular sets. Zbl 1330.68231
Berthé, Valérie; Felice, Clelia; Delecroix, Vincent; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina
3
2015
Beyond substitutive dynamical systems: \(S\)-adic expansions. Zbl 1376.37033
Berthé, Valérie; Delecroix, Vincent
26
2014
Connectedness of fractals associated with Arnoux-Rauzy substitutions. Zbl 1326.37007
Berthé, Valérie; Jolivet, Timo; Siegel, Anne
3
2014
Fine costs for Euclid’s algorithm on polynomials and Farey maps. Zbl 1285.11102
Berthé, Valérie; Nakada, Hitoshi; Natsui, Rie; Vallée, Brigitte
2
2014
Fully subtractive algorithm, Tribonacci numeration and connectedness of discrete planes. Zbl 1352.11013
Berthé, Valérie; Domenjoud, Éric; Jamet, Damien; Provençal, Xavier
2
2014
Balance properties of Arnoux-Rauzy words. Zbl 1269.68073
Berthé, Valérie; Cassaigne, Julien; Steiner, Wolfgang
5
2013
Generating discrete planes with substitutions. Zbl 1400.11075
Berthé, Valérie; Bourdon, Jérémie; Jolivet, Timo; Siegel, Anne
4
2013
Critical connectedness of thin arithmetical discrete planes. Zbl 1382.68246
Berthé, Valérie; Jamet, Damien; Jolivet, Timo; Provençal, Xavier
4
2013
Convergence and factor complexity for the Arnoux-Rauzy-Poincaré algorithm. Zbl 1400.11018
Berthé, Valérie; Labbé, Sebastien
1
2013
Multiple GCDs. Probabilistic analysis of the plain algorithm. Zbl 1360.68972
Berthé, Valérie; Creusefond, Jean; Lhote, Loïck; Vallée, Brigitte
1
2013
Substitutive Arnoux-Rauzy sequences have pure discrete spectrum. Zbl 1313.37004
Berthé, Valérie; Jolivet, Timo; Siegel, Anne
5
2012
Selfdual substitutions in dimension one. Zbl 1252.68164
Berthé, Valérie; Frettlöh, Dirk; Sirvent, Victor
1
2012
Brun expansions of stepped surfaces. Zbl 1236.11011
Berthé, Valérie; Fernique, Thomas
8
2011
Fractal tiles associated with shift radix systems. Zbl 1221.11018
Berthé, Valérie; Siegel, Anne; Steiner, Wolfgang; Surer, Paul; Thuswaldner, Jörg M.
8
2011
Multidimensional Euclidean algorithms, numeration and substitutions. Zbl 1273.11014
Berthé, Valerie
7
2011
An arithmetic and combinatorial approach to three-dimensional discrete lines. Zbl 1272.52019
Berthé, Valérie; Labbé, Sébastien
5
2011
Uniformly balanced words with linear complexity and prescribed letter frequencies. Zbl 1331.68161
Berthé, Valérie; Labbé, Sébastien
3
2011
Combinatorics, automata, and number theory. Zbl 1197.68006
Berthé, Valérie; Rigo, Michel
23
2010
Substitutions, Rauzy fractals and tilings. Zbl 1247.37015
Berthé, Valérie; Siegel, Anne; Thuswaldner, Jörg
12
2010
Diophantine approximation, Ostrowski numeration and the double-base number system. Zbl 1221.11017
Berthé, Valérie; Imbert, Laurent
4
2009
Arithmetic discrete planes are quasicrystals. Zbl 1261.52013
Berthé, Valérie
2
2009
Discrete geometry and symbolic dynamics. Zbl 1204.37011
Berthé, Valérie
1
2009
On an involution of Christoffel words and Sturmian morphisms. Zbl 1213.68476
Berthé, Valérie; de Luca, Aldo; Reutenauer, Christophe
29
2008
Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions. Zbl 1190.11005
Akiyama, Shigeki; Barat, Guy; Berthé, Valérie; Siegel, Anne
15
2008
Sturm numbers and substitution invariance of 3iet words. Zbl 1202.11021
Arnoux, Pierre; Berthé, Valérie; Masáková, Zuzana; Pelantová, Edita
5
2008
On substitution invariant Sturmian words: an application of Rauzy fractals. Zbl 1140.11014
Berthé, Valérie; Ei, Hiromi; Ito, Shunji; Rao, Hui
13
2007
Functional stepped surfaces, flips, and generalized substitutions. Zbl 1119.68136
Arnoux, Pierre; Berthé, Valérie; Fernique, Thomas; Jamet, Damien
12
2007
Purely periodic \(\beta \)-expansions in the Pisot non-unit case. Zbl 1197.11139
Berthé, Valerie; Siegel, Anne
11
2007
Odometers on regular languages. Zbl 1107.68046
Berthé, Valérie; Rigo, Michel
4
2007
Discrete rotations and symbolic dynamics. Zbl 1115.68119
Berthé, Valérie; Nouvel, Bertrand
1
2007
Initial powers of Sturmian sequences. Zbl 1117.37005
Berthé, Valérie; Holton, Charles; Zamboni, Luca Q.
30
2006
Dynamical directions in numeration. Zbl 1138.37005
Barat, Guy; Berthé, Valérie; Liardet, Pierre; Thuswaldner, Jörg
29
2006
Fractal representation of the attractive lamination of an automorphism of the free group. Zbl 1146.20020
Arnoux, Pierre; Berthé, Valérie; Hilion, Arnaud; Siegel, Anne
9
2006
Tilings associated with beta-numeration and substitutions. Zbl 1139.37008
Berthé, Valérie; Siegel, Anne
32
2005
Interactions between dynamics, arithmetics and combinatorics: the good, the bad, and the ugly. Zbl 1156.37301
Berthé, Valérie; Ferenczi, Sébastien; Zamboni, Luca Q.
17
2005
Smooth words over arbitrary alphabets. Zbl 1077.68082
Berthé, Valérie; Brlek, Srečko; Choquette, Philippe
5
2005
Abstract numeration systems and tilings. Zbl 1156.68443
Berthé, Valérie; Rigo, Michel
5
2005
Two-dimensional iterated morphisms and discrete planes. Zbl 1068.37004
Arnoux, Pierre; Berthé, Valérie; Siegel, Anne
12
2004
Lattices and multi-dimensional words. Zbl 1068.37005
Berthé, Valérie; Tijdeman, Robert
6
2004
Substitutions in dynamics, arithmetics and combinatorics. Zbl 1014.11015
Fogg, N. Pytheas; Berthé, Valérie; Ferenczi, Sébastien; Mauduit, Christian; Siegel, A.
263
2002
Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions. Zbl 1017.11006
Arnoux, Pierre; Berthé, Valérie; Ito, Shunji
21
2002
Balance properties of multi-dimensional words. Zbl 0997.68091
Berthé, Valérie; Tijdeman, Robert
16
2002
Palindromes and two-dimensional Sturmian sequences. Zbl 1002.11026
Berthé, Valérie; Vuillon, Laurent
15
2001
Tilings, quasicrystals, discrete planes, generalized substitutions, and multidimensional continued fractions. Zbl 1017.68147
Arnoux, Pierre; Berthé, Valérie; Ei, Hiromi; Ito, Shunji
14
2001
On the numeration system of Ostrowski. (Autour dy système de numération d’Ostrowski.) Zbl 0994.68100
Berthé, Valérie
11
2001
Tilings and rotations on the torus: A two-dimensional generalization of Sturmian sequences. Zbl 0970.68124
Berthé, Valérie; Vuillon, Laurent
44
2000
On continued fraction expansions in positive characteristic: equivalence relations and some metric properties. Zbl 1024.11050
Berthé, Valérie; Nakada, Hitoshi
22
2000
Sequences of low complexity: Automatic and Sturmian sequences. Zbl 0976.11014
Berthé, Valérie
10
2000
Double sequences of low complexity. (Suites doubles de basse complexité.) Zbl 1018.37010
Berthé, Valérie; Vuillon, Laurent
9
2000
Complexity and linear cellular automata. (Complexité et automates cellulaires linéaires.) Zbl 0988.68116
Berthé, Valérie
4
2000
Covering numbers: Arithmetics and dynamics for rotations and interval exchanges. Zbl 0996.37006
Berthé, Valérie; Chekhova, Nataliya; Ferenczi, Sébastien
5
1999
Three distance theorems and combinatorics on words. Zbl 0997.11051
Alessandri, Pascal; Berthé, Valérie
43
1998
Pascal’s triangle, complexity and automata. (Triangle de Pascal, complexité et automates.) Zbl 0922.11012
Allouche, Jean-Paul; Berthé, Valérie
9
1997
Frequencies of factors of Sturmian sequences. (Fréquences des facteurs des suites sturmiennes.) Zbl 0872.11018
Berthé, Valérie
26
1996
Linear combinations of \(\zeta(s)/ \Pi^ s\) over \(F_ q(x)\) for \(1\leq s\leq q-2\). (Combinaisons linéaires de \(\zeta(s)/ \Pi^ s\) sur \(F_ q(x)\), pour \(1\leq s\leq q-2\).) Zbl 0853.11062
Berthé, Valérie
2
1995
Entropy in deterministic and random systems. Zbl 0884.28014
Berthé, V.
1
1995
Conditional entropy of some automatic sequences. Zbl 0846.11019
Berthé, Valérie
3
1994
Automates et valeurs de transcendance du logarithme de Carlitz. (Automata and transcendental values of the Carlitz logarithm). Zbl 0784.11024
Berthé, Valérie
3
1994
Carlitz \(\zeta\)-function and automata. (Fonction \(\zeta\) de Carlitz et automates.) Zbl 0784.11025
Berthé, Valérie
3
1993
New “automatic” proofs for the transcendence of the Carlitz zeta function. (De nouvelles preuves “automatiques” de transcendance pour la fonction zeta de Carlitz.) Zbl 0788.11020
Berthé, Valérie
2
1992
all top 5

Cited by 588 Authors

46 Berthé, Valérie
21 Thuswaldner, Jörg Maximilian
18 Zamboni, Luca Quardo
15 Pelantová, Edita
15 Zhuravlev, Vladimir Georgievich
14 Reutenauer, Christophe
14 Rigo, Michel
13 Leroy, Julien
12 Ferenczi, Sébastien
12 Perrin, Dominique
12 Steiner, Wolfgang
10 Dolce, Francesco
10 Wen, Zhixiong
9 Kim, Donghan
9 Sirvent, Víctor F.
9 Solomyak, Boris
9 Vuillon, Laurent
8 Adamczewski, Boris
8 Cassaigne, Julien
8 de Luca, Aldo
8 Fernique, Thomas
8 Grimm, Uwe
8 Masáková, Zuzana
8 Noll, Thomas
8 Puzynina, Svetlana
8 Tan, Bo
7 Akiyama, Shigeki
7 Baake, Michael
7 Bugeaud, Yann
7 Ito, Shunji
7 Labbé, Sébastien
7 Mauduit, Christian
7 Moshe, Yossi
7 Rao, Hui
7 Richomme, Gwénaël
7 Shutov, Anton V.
7 Siegel, Anne
6 Arnoux, Pierre
6 Damanik, David
6 Hubert, Pascal
6 Kamae, Teturo
6 Koivusalo, Henna
6 Rindone, Giuseppina
6 Sadun, Lorenzo A.
6 Starosta, Štěpán
6 Surer, Paul
6 Vallée, Brigitte
5 Allouche, Jean-Paul Simon
5 Barge, Marcy M.
5 Bédaride, Nicolas
5 Bufetov, Aleksandr Igorevich
5 Charlier, Emilie
5 Clampitt, David
5 De Felice, Clelia
5 Delecroix, Vincent
5 Durand, Fabien
5 Glen, Amy
5 Haynes, Alan K.
5 Julien, Antoine
5 Lim, Seonhee
5 Nakada, Hitoshi
5 Pavlov, Ronnie
5 Provençal, Xavier
5 Salo, Ville O.
5 Scheicher, Klaus
5 Tijdeman, Robert
5 Walton, James J.
5 Wu, Jun
4 Almeida, Jorge
4 Bernat, Julien
4 Chen, Jin
4 Costa, Alfredo
4 De Luca, Alessandro
4 Drmota, Michael
4 Fici, Gabriele
4 Frettlöh, Dirk
4 Frougny, Christiane
4 Guo, Yingjun
4 Justin, Jacques
4 Krasil’shchikov, V. V.
4 Lemańczyk, Mariusz
4 Messaoudi, Ali
4 Mignosi, Filippo
4 Minervino, Milton
4 Moreira, Carlos Gustavo Tamm de Araujo
4 Natsui, Rie
4 Priebe Frank, Natalie
4 Saari, Kalle
4 Stipulanti, Manon
4 Verger-Gaugry, Jean-Louis
4 Vince, Andrew
4 Wen, Zhi-Ying
4 Xue, Yumei
4 Yassawi, Reem
3 Ambrož, Petr
3 Barat, Guy
3 Barnsley, Michael Fielding
3 Berstel, Jean
3 Bertazzon, Jean-Francois
3 Bezuglyi, Sergey I.
...and 488 more Authors
all top 5

Cited in 145 Serials

94 Theoretical Computer Science
30 Ergodic Theory and Dynamical Systems
24 Annales de l’Institut Fourier
18 European Journal of Combinatorics
17 Discrete Mathematics
16 Transactions of the American Mathematical Society
15 Monatshefte für Mathematik
14 Discrete Applied Mathematics
14 Journal de Théorie des Nombres de Bordeaux
13 Discrete and Continuous Dynamical Systems
13 RAIRO. Theoretical Informatics and Applications
11 Journal of Number Theory
11 Indagationes Mathematicae. New Series
10 Journal d’Analyse Mathématique
10 Advances in Applied Mathematics
9 Proceedings of the American Mathematical Society
9 Topology and its Applications
9 RAIRO. Theoretical Informatics and Applications
8 Israel Journal of Mathematics
8 Advances in Mathematics
8 Journal of Mathematical Sciences (New York)
7 Finite Fields and their Applications
6 Discrete & Computational Geometry
6 International Journal of Algebra and Computation
6 Journal of Mathematics and Music
5 Journal of Mathematical Analysis and Applications
5 Mathematische Zeitschrift
5 International Journal of Foundations of Computer Science
5 St. Petersburg Mathematical Journal
5 International Journal of Number Theory
4 Communications in Mathematical Physics
4 Geometriae Dedicata
4 Journal of Combinatorial Theory. Series A
4 Osaka Journal of Mathematics
4 Information and Computation
4 Chebyshevskiĭ Sbornik
4 Actes des Rencontres du C.I.R.M.
3 Journal of Mathematical Physics
3 Journal of Statistical Physics
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Nonlinearity
3 Acta Arithmetica
3 Mathematika
3 Algorithmica
3 Experimental Mathematics
3 The Electronic Journal of Combinatorics
3 Theory of Computing Systems
3 Journal of the European Mathematical Society (JEMS)
3 Annales Henri Poincaré
3 Integers
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 American Mathematical Monthly
2 Bulletin of the Australian Mathematical Society
2 Mathematical Notes
2 Mathematics of Computation
2 Chaos, Solitons and Fractals
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Canadian Journal of Mathematics
2 Journal of Algebra
2 Journal of Approximation Theory
2 Journal of Functional Analysis
2 Journal of Pure and Applied Algebra
2 Quaestiones Mathematicae
2 Semigroup Forum
2 Journal of Symbolic Computation
2 Pattern Recognition
2 Russian Mathematics
2 Fractals
2 Journal of Difference Equations and Applications
2 Chaos
2 Dynamical Systems
2 Stochastics and Dynamics
2 Proceedings of the Steklov Institute of Mathematics
2 Science China. Mathematics
2 Bulletin of Mathematical Sciences
2 Journal of Fractal Geometry
1 Communications in Algebra
1 Information Processing Letters
1 Letters in Mathematical Physics
1 Physica A
1 Studia Mathematica
1 Arkiv för Matematik
1 Algebra Universalis
1 Applied Mathematics and Computation
1 Bulletin of the London Mathematical Society
1 Bulletin de la Société Mathématique de France
1 Colloquium Mathematicum
1 Computing
1 Duke Mathematical Journal
1 Functiones et Approximatio. Commentarii Mathematici
1 International Journal of Mathematics and Mathematical Sciences
1 Inventiones Mathematicae
1 Journal of Computer and System Sciences
1 Journal für die Reine und Angewandte Mathematik
1 Manuscripta Mathematica
1 Mathematische Annalen
1 Mathematica Scandinavica
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Proceedings of the London Mathematical Society. Third Series
1 Siberian Mathematical Journal
...and 45 more Serials
all top 5

Cited in 45 Fields

293 Computer science (68-XX)
262 Dynamical systems and ergodic theory (37-XX)
245 Number theory (11-XX)
79 Convex and discrete geometry (52-XX)
72 Measure and integration (28-XX)
62 Combinatorics (05-XX)
27 Group theory and generalizations (20-XX)
16 General topology (54-XX)
12 General and overarching topics; collections (00-XX)
10 Mathematical logic and foundations (03-XX)
10 Operator theory (47-XX)
10 Information and communication theory, circuits (94-XX)
8 Manifolds and cell complexes (57-XX)
7 General algebraic systems (08-XX)
7 Probability theory and stochastic processes (60-XX)
7 Statistical mechanics, structure of matter (82-XX)
6 Harmonic analysis on Euclidean spaces (42-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Functional analysis (46-XX)
4 Algebraic geometry (14-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Functions of a complex variable (30-XX)
4 Geometry (51-XX)
4 Statistics (62-XX)
4 Numerical analysis (65-XX)
3 Commutative algebra (13-XX)
3 Associative rings and algebras (16-XX)
3 Real functions (26-XX)
3 Partial differential equations (35-XX)
3 Difference and functional equations (39-XX)
3 Sequences, series, summability (40-XX)
3 Algebraic topology (55-XX)
3 Quantum theory (81-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Field theory and polynomials (12-XX)
2 \(K\)-theory (19-XX)
2 Topological groups, Lie groups (22-XX)
2 Operations research, mathematical programming (90-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Integral equations (45-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Mechanics of particles and systems (70-XX)
1 Mechanics of deformable solids (74-XX)
1 Optics, electromagnetic theory (78-XX)

Citations by Year

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