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.
"Finite and Infinite Arithmetic Progressions Related to Beta-Expansion." Abstr. Appl. Anal. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/678769