14 citations · 90 across the 12 of their papers we have counts for
12 papers
A characterization of Sturmian sequences by indistinguishable asymptotic pairs
Sebastián Barbieri, Sébastien Labbé, Štěpán Starosta
We give a new characterization of biinfinite Sturmian sequences in terms of indistinguishable asymptotic pairs. Two asymptotic sequences on a full -shift are indistingu…
Substitutive structure of Jeandel-Rao aperiodic tilings
Sébastien Labbé
Jeandel and Rao proved that 11 is the size of the smallest set of Wang tiles, i.e., unit squares with colored edges, that admit valid tilings (contiguous edges of adjacent tiles ha…
A self-similar aperiodic set of 19 Wang tiles
Sébastien Labbé
We define a Wang tile set of cardinality 19 and show that the set of all valid Wang tilings is self-similar, aperiodic an…
A Set of Sequences of Complexity
Julien Cassaigne, Sébastien Labbé, Julien Leroy
We prove the existence of a ternary sequence of factor complexity for any given vector of rationally independent letter frequencies. Such sequences are constructed from an i…
On the Zero Defect Conjecture
Sébastien Labbé, Edita Pelantová, Štěpán Starosta
Brlek et al. conjectured in 2008 that any fixed point of a primitive morphism with finite palindromic defect is either periodic or its palindromic defect is zero. Bucci and Vaslet…
-dimensional Continued Fraction Algorithms Cheat Sheets
Sébastien Labbé
Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applicati…
Palindromic sequences generated from marked morphisms
Sébastien Labbé, Edita Pelantová
Fixed points of marked and primitive morphisms over arbitrary alphabet are considered. We show that if is palindromic, i.e., its language contain…
Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré Algorithm
Valérie Berthé, Sébastien Labbé
The Arnoux-Rauzy-Poincaré multidimensional continued fraction algorithm is obtained by combining the Arnoux-Rauzy and Poincaré algorithms. It is a generalized Euclidean algorithm.…
A d-dimensional extension of Christoffel words
Sébastien Labbé, Christophe Reutenauer
In this article, we extend the definition of Christoffel words to directed subgraphs of the hypercubic lattice in arbitrary dimension that we call Christoffel graphs. Christoffel g…
A counterexample to a question of Hof, Knill and Simon
Sébastien Labbé
In this article, we give a negative answer to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite…
Uniformly balanced words with linear complexity and prescribed letter frequencies
Valérie Berthé, Sébastien Labbé
We consider the following problem. Let us fix a finite alphabet A; for any given d-uple of letter frequencies, how to construct an infinite word u over the alphabet A satisfying th…
On the critical exponent of generalized Thue-Morse words
Alexandre Blondin-Massé, Srecko Brlek, Amy Glen +1
For certain generalized Thue-Morse words t, we compute the "critical exponent", i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine e…