Non-Standard Numeration Systems
We study some properties of non-standard numeration systems with an irrational base ß >1, based on the so-called beta-expansions of real numbers [1]. We discuss two important properties of these systems, namely the Finiteness property, stating whether the set of finite expansions in a given syste...
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CTU Central Library
2005-01-01
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| Series: | Acta Polytechnica |
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| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/762 |
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doaj-97681982ab704e49b33f1cd509724ac62020-11-24T23:16:50ZengCTU Central LibraryActa Polytechnica1210-27091805-23632005-01-01455762Non-Standard Numeration SystemsP. AmbrožWe study some properties of non-standard numeration systems with an irrational base ß >1, based on the so-called beta-expansions of real numbers [1]. We discuss two important properties of these systems, namely the Finiteness property, stating whether the set of finite expansions in a given system forms a ring, and then the problem of fractional digits arising under arithmetic operations with integers in a given system. Then we introduce another way of irrational representation of numbers, slightly different from classical beta-expansions. Here we restrict ourselves to one irrational base – the golden mean ? – and we study the Finiteness property again. https://ojs.cvut.cz/ojs/index.php/ap/article/view/762numeration systembeta expansiontau-adic expansion |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
P. Ambrož |
| spellingShingle |
P. Ambrož Non-Standard Numeration Systems Acta Polytechnica numeration system beta expansion tau-adic expansion |
| author_facet |
P. Ambrož |
| author_sort |
P. Ambrož |
| title |
Non-Standard Numeration Systems |
| title_short |
Non-Standard Numeration Systems |
| title_full |
Non-Standard Numeration Systems |
| title_fullStr |
Non-Standard Numeration Systems |
| title_full_unstemmed |
Non-Standard Numeration Systems |
| title_sort |
non-standard numeration systems |
| publisher |
CTU Central Library |
| series |
Acta Polytechnica |
| issn |
1210-2709 1805-2363 |
| publishDate |
2005-01-01 |
| description |
We study some properties of non-standard numeration systems with an irrational base ß >1, based on the so-called beta-expansions of real numbers [1]. We discuss two important properties of these systems, namely the Finiteness property, stating whether the set of finite expansions in a given system forms a ring, and then the problem of fractional digits arising under arithmetic operations with integers in a given system. Then we introduce another way of irrational representation of numbers, slightly different from classical beta-expansions. Here we restrict ourselves to one irrational base – the golden mean ? – and we study the Finiteness property again. |
| topic |
numeration system beta expansion tau-adic expansion |
| url |
https://ojs.cvut.cz/ojs/index.php/ap/article/view/762 |
| work_keys_str_mv |
AT pambroz nonstandardnumerationsystems |
| _version_ |
1725586191101722624 |