[en] We present the Maximal Digit Property of alternate base numeration systems, and show that it is equivalent to several interesting properties of those systems: Equality between spectra and beta-integers, optimality of representations, confluence of an associated rewriting system, and the possibility of normalizing representations with this rewriting system.
In doing so, we generalize to an alternate base and merge several notions that were studied independently for Rényi bases.
Joint work with Émilie Charlier, Zuzana Masáková and Edita Pelantová.
