论文标题
埃勒里亚分支贪婪的贪婪多项式的根独立性的几何证明
A geometric proof for the root-independence of the greedoid polynomial of Eulerian branching greedoids
论文作者
论文摘要
我们定义了定期定向的矩阵的根部多层，并证明植根于顶点$ v_0 $的欧拉分支贪婪的贪婪多项式等于$ h^*$ - 图形Matroid双重多样性的$ h^*$多样性。 由于根部多层的定义独立于顶点$ v_0 $，因此这为欧拉分支分支贪婪的贪婪多项式的根独立性提供了几何证明，这一事实首先由Swee Hong Chan，KévinPerrot和Trung Van Pham使用SandPile模型证明。我们还可以获得，如果我们扭转了欧拉（Eulerian Digraph）的每个边缘，则贪婪多项式不会改变。
We define the root polytope of a regular oriented matroid, and show that the greedoid polynomial of an Eulerian branching greedoid rooted at vertex $v_0$ is equivalent to the $h^*$-polynomial of the root polytope of the dual of the graphic matroid. As the definition of the root polytope is independent of the vertex $v_0$, this gives a geometric proof for the root-independence of the greedoid polynomial for Eulerian branching greedoids, a fact which was first proved by Swee Hong Chan, Kévin Perrot and Trung Van Pham using sandpile models. We also obtain that the greedoid polynomial does not change if we reverse every edge of an Eulerian digraph.
