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On the context-freeness of the \(\theta\)-expansions of the integers. (English) Zbl 1041.11008

Summary: Let \(\theta >1\) be a nonintegral real number such that the \(\theta\)-expansion of every positive integer is finite. If the set of \(\theta\)-expansions of all the positive integers is a context-free language, then \(\theta\) must be a quadratic Pisot unit.

MSC:

11A63 Radix representation; digital problems
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
68Q45 Formal languages and automata
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[1] DOI: 10.1017/S0143385700007057 · Zbl 0814.68065
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