A simple proof of the group-theoretic Zhang-Yeung inequality

Harold Nieuwboer; Lubashan Pathirana

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arXiv · 2609.35451

A simple proof of the group-theoretic Zhang-Yeung inequality

Harold Nieuwboer·Lubashan Pathirana

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Abstract

Zhang and Yeung (IEEE Trans. Inf. Theory, 1998) established the first non-Shannon-type inequality that holds for all entropic vectors. Chan and Yeung (IEEE Trans. Inf. Theory, 2002) showed that there is a one-to-one relation between linear entropy inequalities and multiplicative inequalities involving cardinalities of subgroups of a finite group. The Shannon inequality admits a simple proof in the group theoretic setting, but a direct proof of the translation of Zhang--Yeung's inequality to the group-theoretic setting remained elusive. We resolve this open problem, giving a direct proof of the group-theoretic Zhang--Yeung inequality for cardinalities of subgroups of finite groups, using elementary group-theoretic and counting arguments.

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Harold Nieuwboer, Lubashan Pathirana. 2026-09-28. A simple proof of the group-theoretic Zhang-Yeung inequality. https://arxiv.org/abs/2609.35451

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