发表机构
Fakultät für Mathematik, Universität Kassel; Fakultät für Mathematik, Ruhr-Universität Bochum（卡塞尔大学数学系; 波鸿鲁尔大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广连通子图排列至超边情形，证明自由超子图排列类更大但存在图性必要条件，并通过布尔建筑集唯一描述排列，刻画单纯排列。
AI 中文摘要
在本文中，我们推广了由Cuntz和Kühne建立的连通子图排列的概念，允许边的基数大于二，并重点关注局部性质。我们证明了自由连通超子图排列的类别大于自由连通子图排列的类别，但存在一个可回溯到图情形的自由性必要条件。此外，我们通过将这些排列与布尔建筑集相关联，获得了它们的唯一描述。我们研究了建筑集的嵌套复形与交集格之间的关系，并刻画了这一新类别中的所有单纯排列。
英文摘要
In this article, we generalize the notion of connected subgraph arrangements, established by Cuntz and Kühne by allowing edges of cardinality greater than two, with a focus on local properties. We show that the class of free connected hypersubgraph arrangements is larger than the class of free connected subgraph arrangements, but that there exists a necessary condition for freeness that refers back to the graphic case. Furthermore, we obtain a unique description of these arrangements by associating them with Boolean building sets. We study the nested complex of the building set in relation to the lattice of intersections, and characterize all simplicial arrangements within this new class.
Comments22 pages, 11 figures
