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Published in:
Paul Erdős: Life and Work Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Dense Difference Sets and Their Combinatorial Structure

Authors : Vitaly Bergelson, Paul Erdős, Neil Hindman, Tomasz Łuczak

Published in: The Mathematics of Paul Erdős I

Publisher: Springer New York

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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.

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previous chapter Classical Results on Primitive and Recent Results on Cross-Primitive Sequences
next chapter Integer Sets Containing No Solution to
Literature
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V. Bergelson, A density statement generalizing Schur’s Theorem, J. Comb. Theory (Series A) 43 (1986), 336–343.MathSciNet
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V. Bergelson, Applications of ergodic theory to combinatorics, Dissertation (in Hebrew), Hebrew University of Jerusalem: 1984.
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V. Bergelson, Sets of recurrence of \({\mathbb{Z}}^{m}\) actions and properties of sets of differences in \({\mathbb{Z}}^{m}\), J. London Math. Soc. (2) 31 (1985), 295–304.
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H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton Univ. Press, Princeton, 1981.MATH
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Metadata
Title
Dense Difference Sets and Their Combinatorial Structure
Authors
Vitaly Bergelson
Paul Erdős
Neil Hindman
Tomasz Łuczak
Copyright Year
2013
Publisher
Springer New York
Book
The Mathematics of Paul Erdős I

Print ISBN: 978-1-4614-7257-5

Electronic ISBN: 978-1-4614-7258-2

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-7258-2_10

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