The Plünnecke-Ruzsa Inequality

Angeliki Koutsoukou-Argyraki and Lawrence C. Paulson

26 May 2022


We formalise Plünnecke's inequality and the Plünnecke-Ruzsa inequality, following the notes by Timothy Gowers: "Introduction to Additive Combinatorics" (2022) for the University of Cambridge. To this end, we first introduce basic definitions and prove elementary facts on sumsets and difference sets. Then, we show two versions of the Ruzsa triangle inequality. We follow with a proof due to Petridis.
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