论文标题
耦合和匹配：Strassen定理上的组合笔记
Couplings and Matchings: Combinatorial notes on Strassen's theorem
论文作者
论文摘要
一些数学定理代表了以不同形式发现的思想。其中一个定理就是霍尔的婚姻定理。该定理等同于组合学和优化理论的其他几个定理，从某种意义上说，这些结果可以很容易地彼此衍生。在本文中，这表明这种等效性扩展到了Strassen定理的有限版本，这是概率措施耦合的著名结果。尽管这种等效性是已知的，但缺乏这一事实的概率或组合证明。将引入一种新颖的组合引理，可用于推断霍尔和斯特拉森的定理。
Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory, in the sense that these results can easily be derived from each other. In this paper it is shown that this equivalence extends to a finite version of Strassen's theorem, a celebrated result on couplings of probability measures. Though this equivalence is known, probabilistic or combinatorial proofs of this fact are lacking. A novel combinatorial lemma will be introduced that can be used to deduce both Hall's and Strassen's theorems.
