Embeddability Properties of Difference Sets

Details Embeddability Properties of Difference Sets Embeddability Properties of Difference Sets

2012-01-27

arxiv.org/abs/1201.5865v1

Mathematics

Logic

Scientific paper

By using nonstandard analysis, we prove embeddability properties of difference sets A-B of sets of integers. (A set A is "embeddable" into B if every finite configuration of A has shifted copies in B.) As corollaries of our main theorem, we obtain improvements of results by I.Z. Ruzsa about intersections of difference sets, and of Jin's theorem (as refined by V. Bergelson, H. Furstenberg and B. Weiss), where a precise bound is given on the number of shifts of A-B which are needed to cover arbitrarily large intervals.

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