On Cobham's theorem

Fabien Durand (1) , Michel Rigo (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 Département de Mathématiques [Liège]

In this chapter we essentially focus on the representation of non-negative integers in a given numeration system. The main role of such a system --- like the usual integer base $k$ numeration system --- is to replace numbers or more generally sets of numbers by their corresponding representations, {\em i.e.}, by words or by languages. First we consider integer base numeration systems to present the main concepts but rapidly we will introduce non-standard systems and their relationships with substitutions.

Mots clés: dynamical systems; substitutions; ultimate periodicity; dynamical systems.; Numeration systems; recognizable sets of integers; Cobham's theorem

Domaines: Systèmes dynamiques [math.DS]; Combinatoire [math.CO]; Logique [math.LO]; Théorie de l'information et codage [math.IT]; Théorie des nombres [math.NT]; Mathématique discrète [cs.DM]; Théorie de l'information [cs.IT]

Fabien Durand, Michel Rigo. On Cobham's theorem. Automata: from Mathematics to Applications, European Math. Soc., 2011. ⟨hal-00605375⟩