发表机构
University of Copenhagen（哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用初等群论和计数方法，为有限群子群基数的群论Zhang-Yeung不等式提供了直接且简单的证明，解决了该领域长期存在的开放问题。
AI 中文摘要
Zhang和Yeung（IEEE Trans. Inf. Theory, 1998）建立了第一个对所有熵向量都成立的非Shannon型不等式。Chan和Yeung（IEEE Trans. Inf. Theory, 2002）证明了线性熵不等式与有限群子群基数之间的乘法不等式存在一一对应关系。Shannon不等式在群论框架下有简单证明，但Zhang-Yeung不等式转化为群论形式后的直接证明一直难以找到。我们解决了这一开放问题，利用初等群论和计数论证，给出了有限群子群基数的群论Zhang-Yeung不等式的直接证明。
英文摘要
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.
Comments7 pages
