2014/05/13 by Ilya D. Shkredov, Shkredov, Ilya D. · 5 citations
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.1405.3132
52 pages
arxiv created 2014/05/13 · openalex publication_date 2014/05/13 · arxiv updated 2014/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper we prove that any sumset or difference set has large E3 energy. Also, we give a full description of families of sets having critical relations between some kind of energies such as Ek, Tk and Gowers norms. In particular, we give criteria for a set to be a 1) set of the form H+L, where H+H is small and L has "random structure", 2) set equals a disjoint union of sets Hj, each Hj has small doubling, 3) set having large subset A' with 2A' is equal to a set with small doubling and |A'+A'| ≈ |A|4 / \E(A).