Properties of the alternate base representations

Depending on the considered base, numbers can be represented differently. Émilie Charlier and I introduced the new theory of the alternate bases representations. In this generalization of the beta representations, we use a p-tuple B₁,B₂,…,Bp as a base to represent any real number in [0,1]. During this presentation I will first recall the theory, already widely studied, of the beta representations. Then, some properties of the alternate base representations will be stated as well as the generalization of Parry's Theorem.