Sums and difference of finite sets. (English) Zbl 1226.11019

The problem of estimating cardinality of sumsets is one of the interesting and difficult topics of the additive number theory. In this paper, the authors deal with a particular case of this problem. Let \(A\) and \(B\) be two finite subsets in a given abelian group, by using Plünnecke inequalities as the most important tool, they consider the question of comparing the size of \(A-B\) with that of \(A+B\) and the one of estimating the ratio \(|X-B|/|X|\) when \(X\) runs over all the non-empty subsets of \(A\), where \(A\) and \(B\) satisfy the small sumset condition \(|A+B|\leq k|A|\) .


11B13 Additive bases, including sumsets
11B75 Other combinatorial number theory
11P70 Inverse problems of additive number theory, including sumsets
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