论文标题
$ h^*$ - 使用跨树木的活动的图形载体
$h^*$-vectors of graph polytopes using activities of dissecting spanning trees
论文作者
论文摘要
半平衡挖掘图的图形和根系的对称边缘多面是两类的晶格多型，它们的$ h^*$ - 多项式具有有趣的属性，并概括了重要的图形多项式。对于两类的多面体，都有大型自然的解剖类别成单模型的简单。这些简单使其对应于某些跨越树。 我们表明，对于图形的对称边缘多型的任何``跨树解剖''或半平衡挖掘机的根多型，可以将$ h^*$ - 多层型的多项式计算为相应跨越树的某些活动的生成函数。除了提供简单而灵活的算法以计算这些多项式外，我们的结果还表明，所有相关的解剖都彼此相似，这是相似的：事实证明，跨越树剖析的许多统计数据的分布实际上与实际的解剖无关。
Symmetric edge polytopes of graphs and root polytopes of semi-balanced digraphs are two classes of lattice polytopes whose $h^*$-polynomials have interesting properties and generalize important graph polynomials. For both classes of polytopes there are large, natural classes of dissections into unimodular simplices. These are such that the simplices correspond to certain spanning trees. We show that for any ``spanning tree dissection'' of the symmetric edge polytope of a graph, or the root polytope of a semi-balanced digraph, the $h^*$-polynomial of the polytope can be computed as a generating function of certain activities of the corresponding spanning trees. Apart from giving simple and flexible algorithms for computing these polynomials, our results also reveal that all dissections in question are surprisingly similar to each other: It turns out that the distributions of many statistics of spanning tree dissections are in fact independent of the actual dissection.
