The Plünnecke–Ruzsa Inequality: An Overview
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.
KeywordsSumsets Plünnecke–Ruzsa inequality
The author would like to thank Seva Lev, Mel Nathanson and Tom Sanders for their encouragement.
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