Integers in number systems with positive and negative quadratic Pisot base

Zuzana Masáková, Tomáš Vávra

We consider numeration systems with base $\beta$ and $-\beta$, for quadratic Pisot numbers $\beta$ and focus on comparing the combinatorial structure of the sets ${\mathbb{Z}}_{\beta }$ and ${\mathbb{Z}}_{-\beta }$ of number…