5 papers
On modulo-recurrence and window complexity in infinite words
Julien Cassaigne, Idrissa Kaboré
In this paper, we introduce the notions of uniform modulo-recurrence and strong modulo-recurrence. We show that Sturmian words and maximal complexity words are strongly modulo-recu…
The complexity of smooth words over binary alphabets
Julien Cassaigne, Raphaël Henry
Smooth sequences over an alphabet of positive integers are sequences that are infinitely derivable, the emblematic example being the Oldenburger-Kolakoski sequence ov…
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…
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…
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…