Expander graphs in general, and Ramanujan graphs in particular, have been of great interest in the last four decades with many applications in computer science, combinatorics and even pure mathematics. In these notes we describe various efforts made in recent years to generalize these notions from graphs to higher dimensional simplicial complexes.

中文翻译：

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Ramanujan复合物和高维膨胀剂

在过去的四十年中，一般的扩展器图，特别是Ramanujan图，在计算机科学，组合数学甚至纯数学中都有许多应用，引起了人们的极大兴趣。在这些注释中，我们描述了近年来为将这些概念从图推广到高维简单复形所做的各种努力。