Finite and Infinite Arithmetic Progressions Related to Beta-Expansion

Bing Li and Chao Ma

Abstract and Applied Analysis, 2014, vol. 2014, 1-6

Abstract:

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

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:678769

DOI: 10.1155/2014/678769

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