Reiher, Rödl and Schacht showed that the uniform Turán density of every 3-uniform hypergraph is either 0 or at least 1/27, and asked whether there exist 3-uniform hypergraphs with uniform Turán density equal or arbitrarily close to 1/27. We construct 3-uniform hypergraphs with uniform Turán density equal to 1/27.

中文翻译：

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具有最小正均匀图兰密度的超图

Reiher、Rödl 和 Schacht 证明，每个 3-均匀超图的均匀 Turán 密度要么为 0，要么至少为 1/27，并询问是否存在均匀 Turán 密度等于或任意接近 1/27 的 3-均匀超图。我们构造 3-均匀超图，其均匀 Turán 密度等于 1/27。