Prépublications - Preprints

Three characterizations of a self-similar aperiodic 2-dimensional subshift, 65 p., arXiv:2012.03892 (v3: Sep 2024).

Metallic mean Wang tiles II: the dynamics of an aperiodic computer chip, 45 p., arXiv:2403.03197 (March 2024).

Metallic mean Wang tiles I: self-similarity, aperiodicity and minimality, 60 p., arXiv:2312.03652 (v2: March 2024).

Livres - Book (as Editor)

Marthe Bonamy, Xavier Goaoc, Fredrik Johansson, Jérôme Leroux, Marni Mishna, Irena Penev et Sylvain Schmitz, Informatique Mathématique une photographie en 2020, CNRS Éditions, Sébastien Labbé et Vincent Penelle (éd.), paru le 23 mars 2020, 214 pages. ISBN: 9782271134134

Articles

Dumont-Thomas complement numeration systems for \(\mathbb{Z}\), with Jana Lepšová, Integers (2024) #A112 (27 pages), doi:10.5281/zenodo.14340125, arXiv:2302.14481

Indistinguishable asymptotic pairs and multidimensional Sturmian configurations, with Sebastián Barbieri, Ergodic Theory and Dynamical Systems (2024) 1-59, doi:10.1017/etds.2024.39, arXiv:2204.06413

A \(q\)-analog of the Markoff injectivity conjecture holds, with Mélodie Lapointe and Wolfgang Steiner, Algebraic Combinatorics 6 (2023) 1677-1685. doi:10.5802/alco.322, arXiv:2212.09852

A Fibonacci analogue of the two's complement numeration system, with Jana Lepšová, RAIRO - Theoretical Informatics and Applications 57 (2023) 12, 23 pages doi:10.1051/ita/2023007, arXiv:2205.02574

Nonexpansive directions in the Jeandel-Rao Wang shift, with Casey Mann and Jennifer McLoud-Mann, Discrete and Continuous Dynamical Systems, 43 (2023) 3213-3250. doi:10.3934/dcds.2023046, arXiv:2206.02414

Almost everywhere balanced sequences of complexity \(2n+1\), with Julien Cassaigne and Julien Leroy, Moscow Journal of Combinatorics and Number Theory 11 (2022) 287-333. doi:10.2140/moscow.2022.11.287, arXiv:2102.10093.

The \(q\)-analog of the Markoff injectivity conjecture over the language of a balanced sequence, with Mélodie Lapointe, Combinatorial Theory 2 (2022) #9, 25 pages, doi:10.5070/C62156881, arXiv:2106.15886.

Rauzy induction of polygon partitions and toral \(\mathbb{Z}^2\)-rotations, Journal of Modern Dynamics 17 (2021) 481-528. doi:10.3934/jmd.2021017, arXiv:1906.01104, Jupyter notebook.

A characterization of Sturmian sequences by indistinguishable asymptotic pairs, with Sebastián Barbieri and Štěpán Starosta, European Journal of Combinatorics 95 (2021) 103318 doi:10.1016/j.ejc.2021.103318, arXiv:2011.08112

Markov partitions for toral \(\mathbb{Z}^2\)-rotations featuring Jeandel-Rao Wang shift and model sets, Annales Henri Lebesgue 4 (2021) 283-324. doi:10.5802/ahl.73, arXiv:1903.06137

Substitutive structure of Jeandel-Rao aperiodic tilings, Discrete & Computational Geometry 65 (2021) 800-855. doi:10.1007/s00454-019-00153-3, arXiv:1808.07768. Jupyter notebook.

A self-similar aperiodic set of 19 Wang tiles, Geometriae Dedicata 201 (2019) 81-109 doi:10.1007/s10711-018-0384-8, arXiv:1802.03265

A note on matrices mapping a positive vector onto its element-wise inverse, Journal of Mathematical Analysis and Applications 463 (2018) 235-241. doi:10.1016/j.jmaa.2018.03.016, arXiv:1708.06648

On some symmetric multidimensional continued fraction algorithms (with Pierre Arnoux), Ergodic Theory and Dynamical Systems 38 (2018) 1601-1626. doi:10.1017/etds.2016.112, arXiv:1508.07814

On the Zero Defect Conjecture (with Edita Pelantová, Štěpán Starosta), European Journal of Combinatorics 62 (2017) 132-146. [arxiv, doi]

Palindromic sequences generated from marked morphisms (with E. Pelantová), European Journal of Combinatorics 51 (2016) 200-214. [arXiv, doi]

A d-dimensional extension of Christoffel words (with C. Reutenauer), Discrete & Computational Geometry 54 (2015) 152-181. [arXiv, doi]

Factor Complexity of S-adic words generated by the Arnoux-Rauzy-Poincaré Algorithm (with V. Berthé), Advances in Applied Mathematics 63 (2015) 90-130. [arXiv, doi]

A Counterexample to a Question of Hof, Knill and Simon, Electronic Journal of Combinatorics 21 (2014) #P3.11. [arXiv, doi]

Combinatorial properties of double square tiles (with A. Blondin Massé, A. Garon), Theoretical Computer Science 502 (2013) 98-117. [doi]

Complexity of the Fibonacci snowflakes (with A. Blondin-Massé, S. Brlek, M. Mendès France), Fractals 20 (2012) 257. [doi]

A parallelogram tile fills the plane by translation in at most two distinct ways (with A. Blondin Massé, S. Brlek), Discrete Applied Mathematics 160 (2012) 1011-1018. [doi]

Palindromic complexity of codings of rotations (with A. Blondin Massé, S. Brlek, L. Vuillon), Theoret. Comput. Sci. 412 (2011) 6455-6463. [doi]

Sage, un logiciel libre de mathématiques, Bulletin de l'AMQ, Vol. 51, no 2, mai 2011, 59-67.

Two infinite families of polyominoes that tile the plane by translation in two distinct ways (with A. Blondin Massé, S. Brlek, A. Garon), Theoret. Comput. Sci. 412 (2011) 4778-4786. [doi]

Equations on palindromes and circular words (with A. Blondin Massé, S. Brlek, A. Garon), Theoret. Comput. Sci. 412 (2011) 2922-2930. [doi]

Fibonacci snowflakes (with A. Blondin Massé, S. Brlek, M. Mendès France), Ann. Sci. Math. Québec 35 (2011), no 2, 141-152.

Combinatorial properties of f-palindromes in the Thue-Morse sequence (with A. Blondin Massé, S. Brlek, A. Garon), PUMA 19 (2008) 39-52.

On the Critical Exponent of Generalized Thue-Morse Words (with A. Blondin-Massé, S. Brlek, A. Glen), Discrete Math. Theor. Comput. Sci. 9 (2007) 293-304.

Sur le théorème de Pick (with F. Dubeau), Ann. Sci. Math. Québec 29 (2005) 147-166.

Unpublished preprints

3-dimensional Continued Fraction Algorithms Cheat Sheets, November 2015, 9 p. [arxiv, HD pdf version, source code]

A Perron theorem for matrices with negative entries and applications to Coxeter groups (with Jean-Philippe Labbé), November 2015, 14 p. [arxiv]

Actes de conférences - Proceedings

Tristan Roussillon, Sébastien Labbé. Decomposition of Rational Discrete Planes. Third International Joint Conference on Discrete Geometry and Mathematical Morphology, Sara Brunetti and Andrea Frosini and Simone Rinaldi, Apr 2024, Florence (IT), Italy. pp.54-66. [hal-04715762, doi]

Labbé S., Lepšová J. (2021) A Numeration System for Fibonacci-Like Wang Shifts. In: Lecroq T., Puzynina S. (eds) Combinatorics on Words. WORDS 2021. Lecture Notes in Computer Science, vol 12847. Springer, Cham. [arXiv:2105.11898, doi]

Castronuovo, Niccolò, Robert Cori, Sébastien Labbé. A Permutation on Words in a Two Letter Alphabet. In Combinatorics on Words, 240-51. Lecture Notes in Computer Science, vol 10432. Springer, Cham, 2017. [doi]

Cassaigne J., Labbé S., Leroy J. (2017) A Set of Sequences of Complexity 2n+1. In: Brlek S., Dolce F., Reutenauer C., Vandomme É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science, vol 10432. Springer, Cham [arXiv:1707.02741, doi]

S. Labbé, J. Leroy, Bispecial Factors in the Brun S-Adic System, 20th International Conference, DLT 2016, Montréal, Canada, July 25-28, 2016, Proceedings Springer LNCS 9840 (2016) 280-292. [doi, orbi]

S. Labbé, C. Reutenauer, A d-dimensional extension of Christoffel words, Reference: 1103-05-156, Symbolic Dynamics and Combinatorics on Words, Meeting #1103: Fall Eastern Sectional Meeting, Halifax, Canada. October 18, 2014.

S. Labbé, C. Reutenauer, A d-dimensional extension of Christoffel words (sciencesconf.org:jm2014:43699), 15th Mons Theoretical Computer Science Days, 23-26 Sep 2014, Nancy (France).

V. Berthé and S. Labbé, Convergence and Factor Complexity for the Arnoux-Rauzy-Poincaré Algorithm, WORDS 2013, Turku, September 16-20 2013.

V. Berthé and S. Labbé, Uniformly balanced words with linear complexity and prescribed letter frequencies, WORDS 2011, Prague, September 12-16 2011.

V. Berthé and S. Labbé, An Arithmetic and Combinatorial Approach to three-dimensional Discrete Lines, DGCI 2011, I. Debled-Rennesson et al. (Eds.): DGCI 2011, LNCS 6607, pp. 47--58. Springer, Heidelberg (2011). Nancy, 6-8 avril 2011.

A. Blondin Massé, A. Garon and S. Labbé, Generation of double square tiles, GASCom 2010 Montréal, 2 au 4 septembre 2010.

A. Blondin Massé, S. Brlek, A. Garon and S. Labbé, Every polyomino yields at most two square tilings, Lattice Path 2010, Italie, 4 au 7 juillet 2010.

A. Blondin Massé, S. Brlek and S. Labbé, Combinatorial aspects of Escher Tilings (poster), FPSAC 2010, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (August 2-6, 2010, San Francisco, USA).

A. Blondin Massé, S. Brlek, A. Garon and S. Labbé, Christoffel and Fibonacci Tiles, DGCI 2009, 15th IAPR International Conference on Discrete Geometry for Computer Imagery (September 30 - October 2 2009, Montreal, Canada) Springer LNCS 5810 (2009) 67-78.

A. Blondin Massé, S. Brlek, A. Garon and S. Labbé, Palindromes and local periodicity, WORDS 2009, the 7th International Conference on Words, (September 14 - 18, 2009, Salerno, Italia) Electronic proceedings.

A. Blondin Massé, S. Brlek, S. Labbé and L. Vuillon, Codings of rotations on two intervals are full (slides), in J. Nesetril and A. Raspaud (Eds) Proc. European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009), September 7 - 11, 2009 (Bordeaux, France) Electronic Notes in Discrete Mathematics 34 (2009) 289-293. [doi]

Nicolas M. Thiéry et al., Sage-Combinat, Free and Practical Software for Algebraic Combinatorics, FPSAC, Hagenberg, Autriche, 22 juillet 2009.

A. Blondin Massé, S. Brlek and S. Labbé, Combinatorial aspects of double squares, Permutation Patterns 2009 (PP2009) July 13 - 17, 2009 (Florence, Italie) 37-43.

A. Blondin Massé, S. Brlek, A. Frosini, S. Labbé and S. Rinaldi, Reconstructing words from a fixed palindromic length sequence, in Giorgio Ausiello, Juhani Karhumäki, Giancarlo Mauri, Eds., Proc. TCS 2008, 5th IFIP International Conference on Theoretical Computer Science (September 8-10, 2008, Milano, Italia) IFIP International Federation for Information Processing (Springer, Boston) Volume 273 (2008) 101-114.

A. Blondin Massé, S. Brlek and S. Labbé, Palindromic lacunas of the Thue-Morse word, Proc. GASCOM 2008 (16-20 June 2008, Bibbiena, Arezzo-Italia) 53-67.

A. Blondin-Massé, S. Labbé, A note on the critical exponent of generalized Thue-Morse words, Sixième conférence internationale sur les mots, Marseille, 17 septembre 2007. ACTES: Proc. of WORDS 2007, p. 57-62.

S. Labbé, Le théorème de Pick, Actes du 47e congrès de l'Association mathématique du Québec 47 (2004), p. 92.

Thèse de doctorat - Thesis

S. Labbé, Structure des pavages, droites discrètes 3D et combinatoire des mots, Thèse de doctorat en Mathématiques, Montréal, UQAM, 2012, 241 p.

Mémoire de maîtrise - Master's thesis

S. Labbé, Propriétés combinatoires des f-palindromes, Mémoire de maîtrise en Mathématiques, Montréal, UQAM, 2008, 113 p.

Courses notes

S. Labbé, Logiciels mathématiques, notes pour le cours de Logiciels mathématiques de l'Université de Liège, 2016-2017.

Rapports de recherche

G. Charbonneau-Jodoin, A. L'Archevêque, S. Labbé, A. Mongeau, P.-G. Plamondon et L.-P. Saumier, Groupes de Weyl associés aux carquois de Dynkin, Département de mathématiques de l'U. de Sherbrooke, rapport no 26, octobre 2005, 13 p.

F. Dubeau et S. Labbé, Caractéristiques d'Euler et théorème de Pick, Département de mathématiques de l'U. de Sherbrooke, rapport no 19, mai 2005, 19 p.

S. Labbé, Sur le théorème de Pick, Département de mathématiques et d'informatique de l'U. de Sherbrooke, rapport no 303, sept. 2003, 22 p.

Autres publications (Voyages, Ultimate)

J. Bougie, M.-C. Gariépy, F. Pedneault, et. al., Disque en jeu!, Office québécois de la langue française, 2012, 91 p.

S. Labbé, Carnets de voyage : L’expérience de l’étranger, Les éditions de l’Université de Sherbrooke, Sherbrooke, 2005, pages 2-9.

S. Labbé, Pol en Afrique, blogue sur mon expérience au Mali en 2006.