Dense Difference Sets and Their Combinatorial Structure

Vitaly Bergelson (), Paul Erdős, Neil Hindman () and Tomasz Łuczak ()
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Vitaly Bergelson: Ohio State University, Department of Mathematics
Paul Erdős: Mathematical Institute of the Hungarian Academy of Sciences
Neil Hindman: Howard University, Department of Mathematics
Tomasz Łuczak: Adam Mickiewicz University, Department of Discrete Mathematics, Faculty of Mathematics and CS

A chapter in The Mathematics of Paul Erdős I, 2013, pp 133-146 from Springer

Abstract: Summary We show that if a set B of positive integers has positive upper density, then its difference set D(B) has extremely rich combinatorial structure, both additively and multiplicatively. If on the other hand only the density of D(B) rather than B is assumed to be positive, one is not guaranteed any multiplicative structure at all and is guaranteed only a modest amount of additive structure.

Keywords: Set Difference; Multiplicative Structure; Measure Preserving System; Nonempty Finite Subset; Current Lemma (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7258-2_10

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DOI: 10.1007/978-1-4614-7258-2_10

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