Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. Multidimensional continued fractions and symbolic codings of toral translations. (English) Zbl 07774923 J. Eur. Math. Soc. (JEMS) 25, No. 12, 4997-5057 (2023). MSC: 37B10 37A30 37A44 11J70 11K50 11A55 11Y65 28A80 PDFBibTeX XMLCite \textit{V. Berthé} et al., J. Eur. Math. Soc. (JEMS) 25, No. 12, 4997--5057 (2023; Zbl 07774923) Full Text: DOI arXiv
Berthé, Valérie; Goulet-Ouellet, Herman On substitutions preserving their return sets. (English) Zbl 07716982 Frid, Anna (ed.) et al., Combinatorics on words. 14th international conference, WORDS 2023, Umeå, Sweden, June 12–16, 2023. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13899, 77-90 (2023). MSC: 68R15 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{H. Goulet-Ouellet}, Lect. Notes Comput. Sci. 13899, 77--90 (2023; Zbl 07716982) Full Text: DOI
Berthé, Valérie On decision problems for substitutions in symbolic dynamics. (English) Zbl 07368094 Schmitz, Sylvain (ed.) et al., Reachability problems. 14th international conference, RP 2020, Paris, France, October 19–21, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12448, 3-19 (2020). MSC: 68Qxx PDFBibTeX XMLCite \textit{V. Berthé}, Lect. Notes Comput. Sci. 12448, 3--19 (2020; Zbl 07368094) Full Text: DOI
Berthé, Valérie; Cecchi Bernales, Paulina Balancedness and coboundaries in symbolic systems. (English) Zbl 1423.68366 Theor. Comput. Sci. 777, 93-110 (2019). MSC: 68R15 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{P. Cecchi Bernales}, Theor. Comput. Sci. 777, 93--110 (2019; Zbl 1423.68366) Full Text: DOI arXiv
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. Geometry, dynamics, and arithmetic of \(S\)-adic shifts. (Géométrie, dynamique, et arithmétique des décalages \(S\)-adiques.) (English. French summary) Zbl 1433.37010 Ann. Inst. Fourier 69, No. 3, 1347-1409 (2019). Reviewer: Thomas B. Ward (Leeds) MSC: 37B10 37B52 37A46 11K31 11K50 28A80 PDFBibTeX XMLCite \textit{V. Berthé} et al., Ann. Inst. Fourier 69, No. 3, 1347--1409 (2019; Zbl 1433.37010) Full Text: DOI arXiv
Berthé, V.; Labbé, S. Factor complexity of \(S\)-adic words generated by the Arnoux-Rauzy-Poincaré algorithm. (English) Zbl 1310.68170 Adv. Appl. Math. 63, 90-130 (2015). Reviewer: Wolfgang Steiner (Sydney) MSC: 68R15 37B10 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{S. Labbé}, Adv. Appl. Math. 63, 90--130 (2015; Zbl 1310.68170) Full Text: DOI arXiv
Berthé, Valérie; Jolivet, Timo; Siegel, Anne Connectedness of fractals associated with Arnoux-Rauzy substitutions. (English) Zbl 1326.37007 RAIRO, Theor. Inform. Appl. 48, No. 3, 249-266 (2014). Reviewer: Christoph Aistleitner (Kobe) MSC: 37B10 68R15 37A45 PDFBibTeX XMLCite \textit{V. Berthé} et al., RAIRO, Theor. Inform. Appl. 48, No. 3, 249--266 (2014; Zbl 1326.37007) Full Text: DOI arXiv
Berthé, Valérie; Lacasse, Annie; Paquin, Geneviève; Provençal, Xavier A study of Jacobi-Perron boundary words for the generation of discrete planes. (English) Zbl 1296.68113 Theor. Comput. Sci. 502, 118-142 (2013). MSC: 68R15 52C35 PDFBibTeX XMLCite \textit{V. Berthé} et al., Theor. Comput. Sci. 502, 118--142 (2013; Zbl 1296.68113) Full Text: DOI
Berthé, Valérie; Jolivet, Timo; Siegel, Anne Substitutive Arnoux-Rauzy sequences have pure discrete spectrum. (English) Zbl 1313.37004 Unif. Distrib. Theory 7, No. 1, 173-197 (2012). MSC: 37A30 37B10 PDFBibTeX XMLCite \textit{V. Berthé} et al., Unif. Distrib. Theory 7, No. 1, 173--197 (2012; Zbl 1313.37004) Full Text: arXiv
Berthé, Valérie About thin arithmetic discrete planes. (English) Zbl 1222.52019 Theor. Comput. Sci. 412, No. 36, 4757-4769 (2011). MSC: 52C20 68U05 52C23 PDFBibTeX XMLCite \textit{V. Berthé}, Theor. Comput. Sci. 412, No. 36, 4757--4769 (2011; Zbl 1222.52019) Full Text: DOI
Berthé, Valérie; Labbé, Sébastien An arithmetic and combinatorial approach to three-dimensional discrete lines. (English) Zbl 1272.52019 Debled-Rennesson, Isabelle (ed.) et al., Discrete geometry for computer imagery. 16th IAPR international conference, DGCI 2011, Nancy, France, April 6–8, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-19866-3/pbk). Lecture Notes in Computer Science 6607, 47-58 (2011). MSC: 52B55 68R15 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{S. Labbé}, Lect. Notes Comput. Sci. 6607, 47--58 (2011; Zbl 1272.52019) Full Text: DOI
Berthé, Valérie Discrete geometry and numeration. (English) Zbl 1480.37022 Actes Rencontres C.I.R.M. 1, No. 1, 17-22 (2009). MSC: 37B10 37B51 37B52 37E15 11A55 52C99 PDFBibTeX XMLCite \textit{V. Berthé}, Actes Rencontres C.I.R.M. 1, No. 1, 17--22 (2009; Zbl 1480.37022) Full Text: DOI Link
Berthé, Valérie Arithmetic discrete planes are quasicrystals. (English) Zbl 1261.52013 Brlek, Srečko (ed.) et al., Discrete geometry for computer imagery. 15th IAPR international conference, DGCI 2009, Montréal, Canada, September 30 – October 2, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04396-3/pbk). Lecture Notes in Computer Science 5810, 1-12 (2009). MSC: 52C23 52C22 68R15 PDFBibTeX XMLCite \textit{V. Berthé}, Lect. Notes Comput. Sci. 5810, 1--12 (2009; Zbl 1261.52013) Full Text: DOI
Berthé, Valérie; Ei, Hiromi; Ito, Shunji; Rao, Hui On substitution invariant Sturmian words: an application of Rauzy fractals. (English) Zbl 1140.11014 Theor. Inform. Appl. 41, No. 3, 329-349 (2007). Reviewer: Francine Blanchet-Sadri (Greensboro) MSC: 11B85 11J70 37B10 68R15 PDFBibTeX XMLCite \textit{V. Berthé} et al., Theor. Inform. Appl. 41, No. 3, 329--349 (2007; Zbl 1140.11014) Full Text: DOI Numdam EuDML
Arnoux, Pierre; Berthé, Valérie; Hilion, Arnaud; Siegel, Anne Fractal representation of the attractive lamination of an automorphism of the free group. (English) Zbl 1146.20020 Ann. Inst. Fourier 56, No. 7, 2161-2212 (2006). Reviewer: Dimitrios Varsos (Athenai) MSC: 20E05 37B10 20E36 05B45 68R15 57M07 PDFBibTeX XMLCite \textit{P. Arnoux} et al., Ann. Inst. Fourier 56, No. 7, 2161--2212 (2006; Zbl 1146.20020) Full Text: DOI Numdam Numdam EuDML
Fogg, N. Pytheas (ed.); Berthé, Valérie (ed.); Ferenczi, Sébastien (ed.); Mauduit, Christian (ed.); Siegel, A. (ed.) Substitutions in dynamics, arithmetics and combinatorics. (English) Zbl 1014.11015 Lecture Notes in Mathematics. 1794. Berlin: Springer. xv, 402 p. EUR 57.95/net; sFr. 96.50; £40.50; $ 76.80 (2002). Reviewer: Jean-Paul Allouche (Orsay) MSC: 11B85 11-02 37-02 05-02 68Q45 68R15 11A55 11A63 11J70 37B10 28D99 37A45 05A17 PDFBibTeX XMLCite \textit{N. P. Fogg} (ed.) et al., Substitutions in dynamics, arithmetics and combinatorics. Berlin: Springer (2002; Zbl 1014.11015) Full Text: DOI Link Backlinks: MO MO
Arnoux, Pierre; Berthé, Valérie; Ito, Shunji Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions. (English) Zbl 1017.11006 Ann. Inst. Fourier 52, No. 2, 305-349 (2002). Reviewer: Takao Komatsu (Tsu, Mie) MSC: 11A55 11J70 40A15 68R15 PDFBibTeX XMLCite \textit{P. Arnoux} et al., Ann. Inst. Fourier 52, No. 2, 305--349 (2002; Zbl 1017.11006) Full Text: DOI Numdam EuDML
Arnoux, Pierre; Berthé, Valérie; Ei, Hiromi; Ito, Shunji Tilings, quasicrystals, discrete planes, generalized substitutions, and multidimensional continued fractions. (English) Zbl 1017.68147 Discrete models: combinatorics, computation, and geometry. Proceedings of the 1st international conference (DM-CCG), Paris, France, July 2-5, 2001. Paris: Maison de l’Informatique et des Mathématiques Discrètes (MIMD), Discrete Math. Theor. Comput. Sci., Proc. AA, 59-78, electronic only (2001). MSC: 68W05 68U05 PDFBibTeX XMLCite \textit{P. Arnoux} et al., in: Discrete models: combinatorics, computation, and geometry. Proceedings of the 1st international conference (DM-CCG), Paris, France, July 2--5, 2001. Paris: Maison de l'Informatique et des Mathématiques Discrètes (MIMD). 59--78 (2001; Zbl 1017.68147) Full Text: EMIS