On univoque Pisot numbers

J. -P. Allouche, C. Frougny, K. G. Hare

We study Pisot numbers $\beta \in (1,2)$ which are univoque, i.e., such that there exists only one representation of 1 as $1={\sum }_{n\ge 1}{s}_n{\beta }^{-n}$, with $s_n\in \{0,1\}$. We p…