58 citations
- Université Sorbonne Paris NordFR8 papers
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math.DS2025
On balance properties of hypercubic billiard words
Nicolas Bédaride, Valérie Berthé, Antoine Julien
This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order…
math.DS2017
Statistics of patterns in typical cut and project sets
Alan Haynes, Antoine Julien, Henna Koivusalo +1
In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic…