Speaker: Émilie Charlier
Abstract: While working on solving a combinatorial problem on linearnumeration systems (such as the one based on the Fibonacci sequence), we encountered a new way to represent real numbers using finitely many real bases in an alternating manner. These new representations, which “were there”, happen to be a natural generalization of the Rényi numeration systems which have been extensively studied since their introduction in the late 1950s. We call these new systems the alternate base numeration systems. As it turns out, various results on Rényi numeration systems extend quite naturally to alternate real bases, covering areas ranging from combinatorics and automata theory to some dynamical and algebraic aspects. However, when passing to alternate real bases, many challenges emerge as some novel phenomena arise. In this talk, we will present an overview of the currently known results on alternate real bases, and even more generally on Cantor real bases.