On the Delone property of (−β)-integers
The (−β)-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. They can be described by infinite words which are fixed points of anti-morphisms. We show that they are not necessarily uniformly discrete and relatively dense in the real numbers.
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2011-08-01
|
| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1108.3640v1 |
| _version_ | 1811248539594915840 |
|---|---|
| author | Wolfgang Steiner |
| author_facet | Wolfgang Steiner |
| author_sort | Wolfgang Steiner |
| collection | DOAJ |
| description | The (−β)-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. They can be described by infinite words which are fixed points of anti-morphisms. We show that they are not necessarily uniformly discrete and relatively dense in the real numbers. |
| first_indexed | 2024-04-12T15:29:52Z |
| format | Article |
| id | doaj.art-0a515baf0e3c418e8c88a12683f25480 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-04-12T15:29:52Z |
| publishDate | 2011-08-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-0a515baf0e3c418e8c88a12683f254802022-12-22T03:27:08ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802011-08-0163Proc. WORDS 201124725610.4204/EPTCS.63.31On the Delone property of (−β)-integersWolfgang SteinerThe (−β)-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. They can be described by infinite words which are fixed points of anti-morphisms. We show that they are not necessarily uniformly discrete and relatively dense in the real numbers.http://arxiv.org/pdf/1108.3640v1 |
| spellingShingle | Wolfgang Steiner On the Delone property of (−β)-integers Electronic Proceedings in Theoretical Computer Science |
| title | On the Delone property of (−β)-integers |
| title_full | On the Delone property of (−β)-integers |
| title_fullStr | On the Delone property of (−β)-integers |
| title_full_unstemmed | On the Delone property of (−β)-integers |
| title_short | On the Delone property of (−β)-integers |
| title_sort | on the delone property of β integers |
| url | http://arxiv.org/pdf/1108.3640v1 |
| work_keys_str_mv | AT wolfgangsteiner onthedelonepropertyofbintegers |