Subsets with Small Sums in Abelian Groups' I: the Vosper Property
Subsets with Small Sums in Abelian Groups' I: the Vosper Property
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DOI：
10.1006/eujc.1995.0113
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发表时间：
1997-07
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影响因子：
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通讯作者：
Y. O. Hamidoune
中科院分区：
文献类型：
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作者：
Y. O. Hamidoune
LetGbe an abelian group containing a finite subsetBsuch that, for every non-empty finite subsetA?G, |A+B|?min(|G|,|A|+|B|-1).We obtain the necessary and sufficient condition for the validity of the stronger property:For every finite subset A?G, such that |A|?2, |A+B|?min(|G|-1,|A|+|B|).We apply our methods to the range of diagonal forms over finite fields, obtaining a new proof of a result of Tietavainen. Our proof works in characteristic 2, where the question was open. We also apply our methods to obtain a new characterization for abelian Cayley graphs for which each minimum cutset originates or ends in a vertex.
