Geodesic
An improved bound on \((A+A)/(A+A)\)
Ben Lund1
1Rutgers University
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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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).
DOI : 10.37236/6231
Classification : 05A05, 52C10, 11B75
Mots-clés : additive combinatorics

Ben Lund  1

1 Rutgers University 
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Ben Lund. An improved bound on \((A+A)/(A+A)\). The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/6231

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