Convolution estimates and the number of disjoint partitions

2017/05/23 by Ivanisvili, Paata · 2 citations
#11B30 #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.08529

Abstract

Let X be a finite collection of sets. We count the number of ways a disjoint union of n-1 subsets in X is a set in X, and estimate this number from above by |X|^c(n) where c(n)=(1-((n-1)ln (n-1))/(nln n) )^-1. This extends the recent result of Kane-Tao, corresponding to the case n=3 where c(3)≈ 1.725, to an arbitrary finite number of disjoint n-1 partitions.

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• On suprema of convolutions on discrete cubes
• Strong Sparsification for 1-in-3-SAT via Polynomial Freiman-Ruzsa

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