Abstract:Unique expansions in non-integer bases q have been investigated in many papers during the last thirty years. They are often conveniently generated by labeled directed graphs. In the first part of this paper we give a precise description of the set of sequences generated by these graphs.Using the description of univoque graphs, the second part of the paper is devoted to the study of multiple expansions. Contrary to the unique expansions, we prove for each j ≥ 2 that the set U j q of numbers having exactly j exp… Show more
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