A new upper bound for finite additive bases

2005/03/13 by Sinan Gunturk, Melvyn B. Nathanson, Gunturk, Sinan +1 · 1 citation
Mathematics · #11B13 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:11B13

paper · pdf · doi:10.48550/arxiv.math/0503241

19 pages; LaTex

arxiv created 2005/03/13 · arxiv updated 2009/12/01

Abstract

Let n(2,k) denote the largest integer n for which there exists a set A of k nonnegative integers such that the sumset 2A contains 0,1,2,...,n-1. A classical problem in additive number theory is to find an upper bound for n(2,k). In this paper it is proved that limsup_k→∞ n(2,k)/k² ≤ 0.4789.

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