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ON MINIMAL ASYMPTOTIC $g$-ADIC BASES

Part of: Sequences and sets

Published online by Cambridge University Press:  05 August 2015

DENGRONG LING  and
MIN TANG
DENGRONG LING
Affiliation:
School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, PR China email [email protected]
MIN TANG*
Affiliation:
School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, PR China email [email protected]
*
✉[email protected]
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Abstract

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Let $g\geq 2$ be a fixed integer. Let $\mathbb{N}$ denote the set of all nonnegative integers and let $A$ be a subset of $\mathbb{N}$. Write $r_{2}(A,n)=\sharp \{(a_{1},a_{2})\in A^{2}:a_{1}+a_{2}=n\}.$ We construct a thin, strongly minimal, asymptotic $g$-adic basis $A$ of order two such that the set of $n$ with $r_{2}(A,n)=2$ has density one.

Keywords

thin basisminimal asymptotic g-adic basis

MSC classification

Primary: 11B13: Additive bases, including sumsets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 374 - 379
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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