Expanders with superquadratic growth

2016/11/16 by Antal Balog, Balog, Antal, Oliver Roche‐Newton +4 · 1 citation
Mathematics · #11B75 #52C10 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.CO #math.NT #msc:11B75 #msc:52C10

paper · pdf · doi:10.48550/arxiv.1611.05251

arxiv created 2016/11/16 · openalex publication_date 2016/11/16 · arxiv updated 2016/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will prove several expanders with exponent strictly greater than 2. For any finite set A ⊂ \mathbb R, we prove the following six-variable expander results: |(A-A)(A-A)(A-A)| ≫ \frac|A|^2+(1)/(8)log^(17)/(16)|A|,
|(A+A)/(A+A)+(A)/(A)| ≫ \frac|A|^2+(2)/(17)log^(16)/(17)|A|,
|(AA+AA)/(A+A)| ≫ \frac|A|^2+(1)/(8)log |A|,
|(AA+A)/(AA+A)| ≫ \frac|A|^2+(1)/(8)log |A|.

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