56 citations · 118 across the 18 of their papers we have counts for
21 papers
Decidability of the isomorphism problem between multidimensional substitutive subshifts
Christopher Cabezas, Julien Leroy
An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological fa…
-adic characterization of minimal dendric shifts
France Gheeraert, Julien Leroy
Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian s…
Almost everywhere balanced sequences of complexity
Julien Cassaigne, Sébastien Labbé, Julien Leroy
We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that…
-adic characterization of minimal ternary dendric shifts
France Gheeraert, Marie Lejeune, Julien Leroy
Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian s…
Decidability of the isomorphism and the factorization between minimal substitution subshifts
Fabien Durand, Julien Leroy
Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able…
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…
Counting Subwords Occurrences in Base-b Expansions
Julien Leroy, Michel Rigo, Manon Stipulanti
We count the number of distinct (scattered) subwords occurring in the base-b expansion of the non-negative integers. More precisely, we consider the sequence co…
Counting the number of non-zero coefficients in rows of generalized Pascal triangles
Julien Leroy, Michel Rigo, Manon Stipulanti
This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomia…
Behavior of digital sequences through exotic numeration systems
Julien Leroy, Michel Rigo, Manon Stipulanti
Many digital functions studied in the literature, e.g., the summatory function of the base- sum-of-digits function, have a behavior showing some periodic fluctuation. Such funct…
Generalized Pascal triangle for binomial coefficients of words
Julien Leroy, Michel Rigo, Manon Stipulanti
We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of ano…
The constant of recognizability is computable for primitive morphisms
Fabien Durand, Julien Leroy
Mossé proved that primitive morphisms are recognizable. In this paper we give a computable upper bound for the constant of recognizability of such a morphism. This bound can be exp…
Asymptotic properties of free monoid morphisms
Emilie Charlier, Julien Leroy, Michel Rigo
Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account.…
Specular sets
Valérie Berthé, Clelia De Felice, Vincent Delecroix +5
We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract general…
Bifix codes and interval exchanges
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We investigate the relation between bifix codes and interval exchange transformations. We prove that the class of natural codings of regular interval echange transformations is clo…
An analogue of Cobham's theorem for graph directed iterated function systems
Emilie Charlier, Julien Leroy, Michel Rigo
Feng and Wang showed that two homogeneous iterated function systems in with multiplicatively independent contraction ratios necessarily have different attractors. In t…
Maximal bifix decoding
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurren…
Acyclic, connected and tree sets
Valerie Berthé, Clelia De Felice, Francesco Dolce +4
Given a set of words, one associates to each word in an undirected graph, called its extension graph, and which describes the possible extensions of on the left and…
An -adic characterization of minimal subshifts with first difference of complexity
Julien Leroy
In [Ergodic Theory Dynam. System, 16 (1996) 663--682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is -adic with $\card S \leq…
The finite index basis property
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbo…
-adic conjecture and Bratteli diagrams
Fabien Durand, Julien Leroy
In this note we apply a substantial improvement of a result of S. Ferenczi on -adic subshifts to give Bratteli-Vershik representations of these subshifts.
Towards a statement of the S-adic conjecture through examples
Fabien Durand, Julien Leroy, Gwénaël Richomme
The -adic conjecture claims that there exists a condition such that a sequence has a sub-linear complexity if and only if it is an -adic sequence satisfying Condition …