| Title:
|
Greedy and lazy representations in negative base systems (English) |
| Author:
|
Hejda, Tomáš |
| Author:
|
Masáková, Zuzana |
| Author:
|
Pelantová, Edita |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
258-279 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider positional numeration systems with negative real base $-\beta$, where $\beta>1$, and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal $(-\beta)$-representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base $\beta^2$ with a non-integer alphabet. This enables us to characterize digit sequences admissible as greedy and lazy $(-\beta)$-representation. Such a characterization allows us to study the set of uniquely representable numbers. In the case that $\beta$ is the golden ratio and the Tribonacci constant, we give the characterization of digit sequences admissible as greedy and lazy $(-\beta)$-representation using a set of forbidden strings. (English) |
| Keyword:
|
numeration systems |
| Keyword:
|
lazy representation |
| Keyword:
|
greedy representation |
| Keyword:
|
negative base |
| Keyword:
|
unique representation |
| MSC:
|
11A63 |
| MSC:
|
11A67 |
| MSC:
|
37B10 |
| idZBL:
|
Zbl 1275.11020 |
| idMR:
|
MR3085396 |
| . |
| Date available:
|
2013-07-22T08:47:30Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143367 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| . |
