Optimal Number Representations in Negative Bases

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00205666" target="_blank" >RIV/68407700:21340/13:00205666 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10474-013-0336-6" target="_blank" >http://dx.doi.org/10.1007/s10474-013-0336-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10474-013-0336-6" target="_blank" >10.1007/s10474-013-0336-6</a>

Result language
angličtina
Original language name
Optimal Number Representations in Negative Bases
Original language description
For a given base $gamma$ and a digit set $B$ we consider optimal representations of a number $x$, as defined by Dajani at al. in 2012. For a non-integer negative base $gamma=-beta<-1$ and the digit set $A_beta:={0,1,dots,lceilbetarceil-1}$ we derive thetransformation which generates the optimal representation, if it exists. We show that -- unlike the case of negative integer base -- almost no $x$ has an optimal representation. For a positive base $gamma=beta>1$ and the alphabet $A_beta$ we provide an alternative proof of statements obtained by Dajani et al.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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