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The Plünnecke–Ruzsa Inequality: An Overview

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Combinatorial and Additive Number Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 101))

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Abstract

In this expository article we present an overview of the Plünnecke–Ruzsa inequality: the known proofs, some of its well-known applications and possible extensions. We begin with the graph-theoretic setting in which Plünnecke and later Ruzsa worked in. The more purely combinatorial proofs of the inequality are subsequently presented. In the concluding sections we discuss the sharpness of the various results presented thus far and possible extensions of the inequality to the non-commutative setting.

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Acknowledgements

The author would like to thank Seva Lev, Mel Nathanson and Tom Sanders for their encouragement.

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Authors and Affiliations

  1. University of Rochester, Rochester, NY, USA

    G. Petridis

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  1. G. Petridis
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Correspondence to G. Petridis .

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Editors and Affiliations

  1. Department of Mathematics, Lehman College (CUNY), Bronx, New York, USA

    Melvyn B. Nathanson

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Petridis, G. (2014). The Plünnecke–Ruzsa Inequality: An Overview. In: Nathanson, M. (eds) Combinatorial and Additive Number Theory. Springer Proceedings in Mathematics & Statistics, vol 101. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1601-6_16

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