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Abstract and Applied Analysis
Volume 2014, Article ID 678769, 6 pages
http://dx.doi.org/10.1155/2014/678769
Research Article

Finite and Infinite Arithmetic Progressions Related to Beta-Expansion

1Department of Mathematics, South China University of Technology, Guangzhou 510640, China
2Department of General Education, Macau University of Science and Technology, Macau

Received 8 May 2014; Accepted 9 August 2014; Published 28 August 2014

Academic Editor: Douglas R. Anderson

Copyright © 2014 Bing Li and Chao Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.