Keevash and Mycroft [\emph{Mem.~Amer.~Math.~Soc., 2015}] developed a geometric theory for hypergraph matchings and characterized the dense simplicial complexes that contain a perfect matching. Their proof uses the hypergraph regularity method and the hypergraph blow-up lemma recently developed by Keevash. In this note we give a new proof of their results, which avoids these complex tools. In particular, our proof uses the lattice-based absorbing method developed by the author and a recent probabilistic argument of Kohayakawa, Person and the author.

中文翻译：

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关于 k-复形中的完美匹配

Keevash 和 Mycroft [\emph{Mem.~Amer.~Math.~Soc., 2015}] 开发了一种用于超图匹配的几何理论，并表征了包含完美匹配的密集单纯复形。他们的证明使用了 Keevash 最近开发的超图正则性方法和超图膨胀引理。在这篇笔记中，我们给出了他们结果的新证明，避免了这些复杂的工具。特别是，我们的证明使用了作者开发的基于格的吸收方法以及 Kohayakawa、Person 和作者最近的概率论证。