On Ruzsa's discrete Brunn-Minkowski conjecture

2023/06/22 by van Hintum, Peter, Keevash, Peter, Tiba, Marius · 1 citation
#11P70 #49Q20 #52A27 #52A40 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.13225

Abstract

We prove a conjecture by Ruzsa from 2006 on a discrete version of the Brunn-Minkowski inequality, stating that for any A,B⊂ℤ^k and ε>0 with B not contained in n_k,ε parallel hyperplanes we have |A+B|^1/k≥ |A|^1/k+(1-ε)|B|^1/k.

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• From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities

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