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May 2010 Fraction Sets for Basic Digit Sets
Darren D. Wick
Missouri J. Math. Sci. 22(2): 91-96 (May 2010). DOI: 10.35834/mjms/1312233138


A finite set of integers $D$ with $0\in D$ is basic for the base $b\in \mathbb Z$ if every $z\in\mathbb Z$ can be written uniquely as an integer in the base $b$ with digits from $D$. Since such a base representation is unsigned, basic sets must have a negative base $b$ or some negative integers in $D$. The fraction set for $(b,D)$ is the set of all representable numbers with integer part zero. We show that if $(b,D)$ is basic and $D$ consists of consecutive digits, then the fraction set is an interval of length one whose endpoints have redundant representations. Furthermore, we show that if $D$ does not consist of consecutive integers, then $F$ is disconnected.


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Darren D. Wick. "Fraction Sets for Basic Digit Sets." Missouri J. Math. Sci. 22 (2) 91 - 96, May 2010.


Published: May 2010
First available in Project Euclid: 1 August 2011

zbMATH: 1209.11016
MathSciNet: MR2675404
Digital Object Identifier: 10.35834/mjms/1312233138

Primary: 11A63

Rights: Copyright © 2010 Central Missouri State University, Department of Mathematics and Computer Science


Vol.22 • No. 2 • May 2010
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