Transit functions serve not only as abstractions of betweenness and convexity but are also closely connected with clustering systems. Here, we investigate the canonical transit functions of binary clustering systems inspired by pyramids, i.e., interval hypergraphs. We provide alternative characterizations of weak hierarchies, and describe union-closed binary clustering systems as a subclass of pyramids and weakly pyramidal clustering systems as an interesting generalization.

翻译：传递函数不仅作为介于性和凸性的抽象概念，还与聚类系统紧密相关。本文研究了受金字塔（即区间超图）启发的二元聚类系统的典范传递函数。我们给出了弱层次结构的替代刻画，将并封闭的二元聚类系统描述为金字塔的一个子类，并将弱金字塔聚类系统描述为一种有趣的推广形式。