3 papers
math.CO2026
Symbols frequencies in the Thue--Morse word in base and related conjectures
Julien Cassaigne, Bastiàn Espinoza, Michel Rigo +1
We study a binary Thue--Morse-type sequence arising from the base- expansion of integers, an archetypal automatic sequence in a rational base numeration system. Because the se…
math.DS2026
Language of a non-minimal billiard trajectory inside a cube
Moussa Barro, Nicolas Bédaride, Julien Cassaigne
We consider a non-minimal billiard trajectory inside the cube. We study the language of the associated orbit when the map is coded with three letters associated to three non-parall…
math.DS2025
Freezing phase transition for the Thue-Morse subshift
Nicolas Bédaride, Julien Cassaigne, Pascal Hubert +1
On the full shift on two symbols, we consider the potential defined by where denotes the longest common prefix between the infinite word and an element…