Embeddability Properties of Difference Sets

Mauro Di Nasso

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arXiv · 1201.5865

Embeddability Properties of Difference Sets

Mauro Di Nasso

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Abstract

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. Fürstenberg 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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BibTeX RIS

Mauro Di Nasso. 2013-12-24. Embeddability Properties of Difference Sets. https://arxiv.org/abs/1201.5865

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