A Weighted Pr\'ekopa-Leindler inequality and sumsets with quasicubes

Autor:	Green, Ben, Matolcsi, Dávid, Ruzsa, Imre, Shakan, George, Zhelezov, Dmitrii
Rok vydání:	2020
Předmět:	Mathematics - Number Theory Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Pr\'ekopa-Leindler inequality. This is then applied to show that if $A, B \subseteq \mathbb{Z}^d$ are finite sets and $U$ is a subset of a "quasicube" then $|A + B + U| \geq |A|^{1/2} |B|^{1/2} |U|$. This result is a key ingredient in forthcoming work of the fifth author and P\"alv\"olgyi on the sum-product phenomenon. Comment: 5 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.04077 Zobrazit plný text záznamu View this record from Arxiv