Marco Pedicini. Greedy expansions and sets with deleted digits.

We generalize a result of Daróczy and Kįtai, on the characterization of univoque numbers with respect to a non-integer base [DaróczyKįta1985] by relaxing the digits alphabet to a generic set of real numbers. We apply the result to derive the construction of a Büchi automata accepting all and only the greedy sequences for a given base and digit set. In the appendix we prove a more general version of the fact that the expansion of an element xin QQ(q) is possibly periodic, if q is a Pisot number.

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