Hypertrees are high-dimensional counterparts of graph theoretic trees. They have attracted a great deal of attention by various investigators. Here we introduce and study Hyperpaths -- a particular class of hypertrees which are high dimensional analogs of paths in graph theory. A $d$-dimensional hyperpath is a $d$-dimensional hypertree in which every $(d-1)$-dimensional face is contained in at most $(d+1)$ faces of dimension $d$. We introduce a possibly infinite family of hyperpaths for every dimension, and investigate its properties in greater depth for dimension $d=2$.

中文翻译：

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超路径

超树是图论树的高维对应物。他们引起了各种调查人员的极大关注。在这里，我们介绍和研究超路径——一种特殊的超树，它是图论中路径的高维模拟。$d$维超路径是一个$d$维超树，其中每个$(d-1)$维面最多包含在$d$维数的$(d+1)$个面中。我们为每个维度引入了一个可能无限的超路径族，并在维度 $d=2$ 上更深入地研究其属性。