Finite and infinite arithmetic progressions related to beta-expansion (Q1724722)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Finite and infinite arithmetic progressions related to beta-expansion |
scientific article; zbMATH DE number 7022865
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite and infinite arithmetic progressions related to beta-expansion |
scientific article; zbMATH DE number 7022865 |
Statements
Finite and infinite arithmetic progressions related to beta-expansion (English)
0 references
14 February 2019
0 references
Summary: Let \(1 < \beta < 2\) and \(\varepsilon(x, \beta)\) be the \(\beta\)-expansion of \(x \in [0,1)\). Denote by \(A_\beta(x)\) the set of positions where the digit 1 appears in \(\varepsilon(x, \beta)\). We consider the sets of points \(x\) such that \(A_\beta(x)\) contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. Their sizes are investigated from the topological, metric, and dimensional viewpoints.
0 references
0 references
