On the dimension group of unimodular -adic subshifts

V Berthe, P Cecchi Bernales, F Durand, J Leroy… - Monatshefte für …, 2021 - Springer
Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor
systems. This paper studies a natural family of minimal Cantor systems having a finitely …

-adic characterization of minimal dendric shifts

F Gheeraert, J Leroy - arxiv preprint arxiv:2206.00333, 2022 - arxiv.org
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 shifts …

Balancedness and coboundaries in symbolic systems

V Berthé, PC Bernales - Theoretical Computer Science, 2019 - Elsevier
This paper studies balancedness for infinite words and subshifts, both for letters and factors.
Balancedness is a measure of disorder that amounts to strong convergence properties for …

How to prove that a sequence is not automatic

JP Allouche, J Shallit, R Yassawi - Expositiones Mathematicae, 2022 - Elsevier
Automatic sequences have many properties that other sequences (in particular, non-
uniformly morphic sequences) do not necessarily share. In this paper we survey a number of …

On substitutions preserving their return sets

V Berthé, H Goulet-Ouellet - International Conference on Combinatorics …, 2023 - Springer
We consider the question of whether or not a given primitive substitution preserves its sets of
return words—or return sets for short. More precisely, we study the property asking that the …

-adic characterization of minimal ternary dendric shifts

F Gheeraert, M Lejeune, J Leroy - Ergodic Theory and Dynamical …, 2022 - cambridge.org
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 shifts …

Substitutions and Cantor real numeration systems

E Charlier, C Cisternino, Z Masáková… - arxiv preprint arxiv …, 2023 - arxiv.org
We consider Cantor real numeration system as a frame in which every non-negative real
number has a positional representation. The system is defined using a bi-infinite sequence …

String attractors and bi-infinite words

P BÊaur, F Gheeraert, BH de Menibus - arxiv preprint arxiv:2403.13449, 2024 - arxiv.org
String attractors are a combinatorial tool coming from the field of data compression. It is a set
of positions within a word which intersects an occurrence of every factor. While one-sided …

On partial rigidity of -adic subshifts

S Donoso, A Maass, T Radić - arxiv preprint arxiv:2312.12406, 2023 - arxiv.org
We develop combinatorial tools to study partial rigidity within the class of minimal $\mathcal
{S} $-adic subshifts. By leveraging the combinatorial data of well-chosen Kakutani-Rokhlin …

Indistinguishable asymptotic pairs and multidimensional Sturmian configurations

S Barbieri, S Labbé - Ergodic Theory and Dynamical Systems, 2025 - cambridge.org
Indistinguishable asymptotic pairs and multidimensional Sturmian configurations Page 1 Ergod.
Th. & Dynam. Sys., page 1 of 59 © The Author(s), 2024. Published by Cambridge University …