An Improved Bound on (A+A)/(A+A)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 16 Sep 2016Embargo end date: 01 Jun 2016Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 23 (eissn: 1077-8926,

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Authors: Ben Lund 0002;

doi: 10.37236/6231 , 10.48550/arxiv.1606.03468

arXiv: 1606.03468

An Improved Bound on (A+A)/(A+A)

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Abstract

We show that, for a finite set $A$ of real numbers, the size of the set$$\frac{A+A}{A+A} = \left\{ \frac{a+b}{c+d} : a,b,c,d \in A, c+d \neq 0 \right \}$$is bounded from below by$$\left|\frac{A+A}{A+A} \right| \gg \frac{|A|^{2+1/4}}{|A / A|^{1/8} \log |A|}.$$This improves a result of Roche-Newton (2016).

Related Organizations

Rutgers, The State University of New Jersey
United States
Rutgers University New Brunswick
United States

Keywords

Permutations, words, matrices, Other combinatorial number theory, FOS: Mathematics, additive combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Erdős problems and related topics of discrete geometry

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