Finite and Infinite Arithmetic Progressions Related to Beta-Expansion
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 si...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/678769 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564864543883264 |
|---|---|
| author | Bing Li Chao Ma |
| author_facet | Bing Li Chao Ma |
| author_sort | Bing Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0494ae3a66514c2ca420d44caa423a49 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0494ae3a66514c2ca420d44caa423a492025-02-03T01:10:00ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/678769678769Finite and Infinite Arithmetic Progressions Related to Beta-ExpansionBing Li0Chao Ma1Department of Mathematics, South China University of Technology, Guangzhou 510640, ChinaDepartment of General Education, Macau University of Science and Technology, MacauLet 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.http://dx.doi.org/10.1155/2014/678769 |
| spellingShingle | Bing Li Chao Ma Finite and Infinite Arithmetic Progressions Related to Beta-Expansion Abstract and Applied Analysis |
| title | Finite and Infinite Arithmetic Progressions Related to Beta-Expansion |
| title_full | Finite and Infinite Arithmetic Progressions Related to Beta-Expansion |
| title_fullStr | Finite and Infinite Arithmetic Progressions Related to Beta-Expansion |
| title_full_unstemmed | Finite and Infinite Arithmetic Progressions Related to Beta-Expansion |
| title_short | Finite and Infinite Arithmetic Progressions Related to Beta-Expansion |
| title_sort | finite and infinite arithmetic progressions related to beta expansion |
| url | http://dx.doi.org/10.1155/2014/678769 |
| work_keys_str_mv | AT bingli finiteandinfinitearithmeticprogressionsrelatedtobetaexpansion AT chaoma finiteandinfinitearithmeticprogressionsrelatedtobetaexpansion |