Abstract

Let 1<β<2. Given any x∈[0,(β−1)−1], a sequence (an)∈{0,1}N is called a β-expansion of x if x=∑∞n=1anβ−n. For any k≥1 and any (b1⋯bk)∈{0,1}k, if there exists some k0 such that ak0+1ak0+2⋯ak0+k=b1⋯bk, then we call (an) a universal β-expansion of x. Sidorov (2003) and Dajani and de Vries (2007) proved that for
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