5 papers
The complexity of smooth words over binary alphabets
Julien Cassaigne, Raphaël Henry
Smooth words over an alphabet of non-negative integers are infinite words that are infinitely derivable, the emblematic example being the Oldenburger-Kolakoski word over…
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…
Symbols frequencies in the Thue--Morse word in base and related conjectures
Julien Cassaigne, Bastià n 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…