论文标题
矩阵多面体的重构
Reconstructibility of matroid polytopes
论文作者
论文摘要
我们指定了从其图形或双图可以重建多层的含义。我们介绍了类重建性的问题，即可以从给定类中的（偶）图确定多层的面部晶格。我们提供了立方多型的示例，这些示例从其双重图中不可重建。此外，我们表明矩阵（基本）多型从其图中不可重建，也不是从其双重图中重新结构的。我们的反例包括超图像。此外，我们证明了Matroid多型从其图中可以重建类，并且我们提出了一种$ O（n^3）$算法，该算法从其$ n $ vertex图中计算出矩阵多层的顶点。此外，我们的证明包括对所有具有同构基础交换图的矩形的表征。
We specify what is meant for a polytope to be reconstructible from its graph or dual graph. And we introduce the problem of class reconstructibility, i.e., the face lattice of the polytope can be determined from the (dual) graph within a given class. We provide examples of cubical polytopes that are not reconstructible from their dual graphs. Furthermore, we show that matroid (base) polytopes are not reconstructible from their graphs and not class reconstructible from their dual graphs; our counterexamples include hypersimplices. Additionally, we prove that matroid polytopes are class reconstructible from their graphs, and we present a $O(n^3)$ algorithm that computes the vertices of a matroid polytope from its $n$-vertex graph. Moreover, our proof includes a characterisation of all matroids with isomorphic basis exchange graphs.
