On the representation of an integer in Ostrowski and recurrence numeration systems

Abstract

We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski-$\hat{I}\pm$ numeration system, where $\hat{I}\pm$ is a quadratic irrational. We prove a similar result for the representation of an integer in two \textit{different} Ostrowski numeration systems.

23 pages, Comments welcome