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组合数学中的熵方法

Entropy methods in combinatorics

Wojciech Samotij

arXiv 2607.24414首次发表:更新:

AI 中文总结

本文围绕组合数学中熵方法展开,对相关工作有选择地概述,详细讨论部分内容并阐述关键思想,展示了熵方法在组合数学领域近年来的应用及发展情况。

AI 中文摘要

尽管熵方法在组合数学中已使用至少五十年,但近年来才真正广泛应用。现在有数十篇(甚至数百篇)组合数学论文关键依赖熵的概念,并利用各种强大的熵恒等式和不等式。在这篇简短的综述文章中,我们对这些工作进行了有选择的概述,并更详细地讨论了其中一些,概述了一些关键思想。

英文摘要

Even though entropy methods have been used in combinatorics for at least five decades, only in recent years has their use really proliferated. There are now tens, if not hundreds, of combinatorial papers that crucially rely on the notion of entropy and exploit the various powerful identities and inequalities relating entropies. In this short survey article, we give a selective overview of these works and discuss several of them in more detail, outlining some of the key ideas.

Comments19 pages; a survey for the ICM

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