On univoque Pisot numbers

We study Pisot numbers $\beta \in (1, 2)$ which are univoque, i.e., such that there exists only one representation of $1$ as $1 = \sum_{n \geq 1} s_n\beta^{-n}$, with $s_n \in \{0, 1\}$. We prove in particular that there exists a smallest univoque Pisot number, which has degree $14$. Furthermore we give the smallest limit point of the set of univoque Pisot numbers.

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