Sums and differences of finite sets

Abstract

In a given abelian group, let $A$ and $B$ be two finite subsets satisfying the small sumset condition $|A+B|\le K|A|$. We consider the problem of estimating how large $|A-B|$ can be in terms of $|A|$ and $K$ and the one of estimating the ratio $|X-B|/|X|$ when $X$ runs over all the non-empty subsets of $A$.

Locations

• Functiones et Approximatio Commentarii Mathematici - View - PDF