Regularity of Positional Numeration Systems Without a Dominant Root

This talk by Emilie Charlier explores the regularity of positional numeration systems without a dominant root, presented at the Workshop on "Uniform Distribution of Sequences" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Discover how non-dominant root positional numeration systems can generate regular numeration languages, building upon Hollander's 1998 work on dominant root systems. Learn about the full and effective characterization of these systems and how they naturally lead to multi-base numeration systems (alternate bases) for representing real numbers. The presentation bridges an important gap in Hollander's description and generalizes the connection between dominant root positional numeration systems for integers and beta-expansions of real numbers.