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From an entropic inequality for sums in abelian groups to the theorems of Ruzsa and Plünnecke
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.
Related
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BibTeX
@misc{nair2026from,
title = {{From an entropic inequality for sums in abelian groups to the theorems of Ruzsa and Plünnecke}},
author = {Chandra Nair and Aref Namayandeh and Zhaobang Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11614},
eprint = {2610.11614},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11614},
}
RIS
TY - UNPB
TI - From an entropic inequality for sums in abelian groups to the theorems of Ruzsa and Plünnecke
AU - Chandra Nair
AU - Aref Namayandeh
AU - Zhaobang Zhu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11614
UR - https://arxiv.org/abs/2610.11614
AB - 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.
ER -