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Geometry, Structure and Randomness in Combinatorics

Embeddability properties of difference sets of integers

speaker: Mauro Di Nasso (Dipartimento di Matematica, Università di Pisa)

abstract: We present 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. The proofs use the methods of nonstandard analysis.

Tue 4 Sep, 15:30 - 16:30, Aula Dini
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