2 papers
math.CO2026
Progressive and Rushed Dyck Paths
Axel Bacher
We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a…
math.DS2026
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…