From an entropic inequality for sums in abelian groups to the theorems of Ruzsa and Pl\"unnecke

2026-10-09来源 arXiv math.ITEnglish

arXiv:2610.11614v1 Announce Type: new Abstract: We give a direct information-theoretic proof of the Pl\"unnecke--Ruzsa inequalities for finite subsets of abelian groups. The argument rests on an elementary coupling inequality proved by maximizing joint entropy, without tensor powers or asymptotic constructions. It also yields Ruzsa's sumset triangle inequality and an extension to non-abelian groups.

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From an entropic inequality for sums in abelian groups to the theorems of Ruzsa and Pl\"unnecke

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