关于连块多面体

Pub Date : 2024-07-11 DOI:10.1007/s00454-024-00675-5

Justus Bruckamp, Markus Chimani, Martina Juhnke

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引用次数: 0

摘要

本文研究的是连通块多面体，它除了本身的优点外，还可以看作是某些基于连通性或欧拉子图多面体的概括。我们提供了该多面体的完整面描述，描述了它的边的特征，并证明它是赫氏多面体。我们还通过构建无平方格罗伯纳基证明了连通块状多面体具有规则的单模态三角剖分。此外，我们还证明了这个多面体是指数为 2 的 Gorenstein 多面体，而且它的\(h^*\)向量是单模态的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Connected Blocks Polytope

In this paper, we study the connected blocks polytope, which, apart from its own merits, can be seen as the generalization of certain connectivity based or Eulerian subgraph polytopes. We provide a complete facet description of this polytope, characterize its edges and show that it is Hirsch. We also show that connected blocks polytopes admit a regular unimodular triangulation by constructing a squarefree Gröbner basis. In addition, we prove that the polytope is Gorenstein of index 2 and that its \(h^*\)-vector is unimodal.

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