From an entropic inequality for sums in abelian groups to the theorems of Ruzsa and Plünnecke
Year: 2026
Type: preprint
Abstract: We give a direct information-theoretic proof of the Plünnecke--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.
Source: arXiv (Cornell University)
Authors: Nair, Chandra, Namayandeh, Aref, Zhu, Zhaobang
Institution: Chinese University of Hong Kong
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221111793