On Finite Difference Sets

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Abstract

We establish a lower estimate of the cardinality of finite difference sets in the three dimensional Euclidean space R3 by showing that ¦AA¦ ≧ 4.5 ¦A¦ -9 for every three dimensional finite set A. In addition, we describe the structure of two and three dimensional sets with the smallest cardinality of the difference set.

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