Difference sets are not multiplicatively closed

Difference sets are not multiplicatively closed, Discrete Analysis 2016:17, 20pp. The famous sum-product problem of Erdős and Szemerédi asks the following. Let $A$ be a set of $n$ real numbers. Define the _sumset_ $A+A$ of $A$ to be the set $\{x+y:x,y\in A\}$ and the _product set_ $A.A$ to be the s...

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Bibliographic Details
Main Author: Ilya Shkredov
Format: Article
Language:English
Published: Diamond Open Access Journals
Series:Discrete Analysis
Online Access:http://discrete-analysis.scholasticahq.com/article/913-difference-sets-are-not-multiplicatively-closed.pdf