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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:
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