In this paper, we prove that for any $k\ge 3$, there exist infinitely many minimal asymmetric k-uniform hypergraphs. This is in a striking contrast to $k=2$, where it has been proved recently that there are exactly 18 minimal asymmetric graphs.

We also determine, for every $k\ge 1$, the minimum size of an asymmetric k-uniform hypergraph.

中文翻译：

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最小不对称超图

在本文中，我们证明对于任意$k\ge 3$，存在无穷多个最小非对称k一致超图。这与$k=2$，最近已证明存在 18 个最小非对称图。

我们还确定，对于每个$k\ge 1$，非对称k均匀超图的最小尺寸。