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2014 Finite and Infinite Arithmetic Progressions Related to Beta-Expansion
Bing Li, Chao Ma
Abstr. Appl. Anal. 2014: 1-6 (2014). DOI: 10.1155/2014/678769


Let 1<β<2 and ε(x,β) be the β-expansion of x[0,1). Denote by Aβ(x) the set of positions where the digit 1 appears in ε(x,β). We consider the sets of points x such that Aβ(x) contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. Their sizes are investigated from the topological, metric, and dimensional viewpoints.


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Bing Li. Chao Ma. "Finite and Infinite Arithmetic Progressions Related to Beta-Expansion." Abstr. Appl. Anal. 2014 1 - 6, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022865
MathSciNet: MR3256253
Digital Object Identifier: 10.1155/2014/678769

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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