Łukasiewicz language and diagonals of formal series. (Langage de Łukasiewicz et diagonales de séries formelles.)
-shift, systèmes de numération et automates
In this note we prove that the language of a numeration system is the language of a -shift under some assumptions on the basis. We deduce from this result a partial answer to the question when the language of a numeration system is regular. Moreover, we give a characterization of the arithmetico-geometric sequences and the mixed radix sequences that are basis of a numeration system for which the language is regular. Finally, we study the Ostrowski systems of numeration and give another proof of...