The Plünnecke-Ruzsa Inequality

Angeliki Koutsoukou-Argyraki 🌐 and Lawrence C. Paulson

May 26, 2022

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Abstract

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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Topics

Theories of Pluennecke_Ruzsa_Inequality