论文标题
整数流的晶格和常规矩阵的紧密连接方向的位置
Lattice of Integer Flows and the Poset of Strongly Connected Orientations for Regular Matroids
论文作者
论文摘要
Amini的2010年结果提供了一种从整数流的晶格的几何形状中提取有关图的结构的信息（该图确定图形最高为两种呈效果）。具体而言，Amini表明，Voronoi polytope的面部面部与强连接的子图方向的poset是同构。这回答了Caporaso和Viviani提出的一个问题，Amini也证明了整数削减的双重结果。在本文中，我们将Amini的结果推广到常规的矩形；在这种情况下，整数剪切定理通过使二元性明确作为矩形偶性，成为整数流的定理的直接结果。
A 2010 result of Amini provides a way to extract information about the structure of the graph from the geometry of the Voronoi polytope of the lattice of integer flows (which determines the graph up to two-isomorphism). Specifically, Amini shows that the face poset of the Voronoi polytope is isomorphic to the poset of strongly connected orientations of subgraphs. This answers a question raised by Caporaso and Viviani, and Amini also proves a dual result for integer cuts. In this paper we generalise Amini's result to regular matroids; in this context the theorem for integer cuts becomes a direct consequence of the theorem for integer flows, by making duality explicit as matroid duality.
