图上的因子，二项式和单项式理想，以及细胞分解
Divisors on graphs, binomial and monomial ideals, and cellular resolutions
摘要：
我们研究各种二项式和单项式理想中出现的理论的因子，方向，和拟阵的图。我们使用的思想从位势论的图形和从理论的Delaunay分解格来描述其最小多面体细胞自由分解。我们发现，所有这些理想的决议是密切相关的，他们的$\mathbb{Z}$分级贝蒂表相吻合。作为推论，我们给出了概念上的证明Postnikov和Shapiro，Manjunath和Sturmfels，以及Perkinson，Perlman和Wilmes提出的问题。其他各种结果有关的理论芯片射击游戏的图形也遵循我们的一般技术和结果。
英文摘要：
We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their $\mathbb{Z}$-graded Betti tables coincide. As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results related to the theory of chip-firing games on graphs also follow from our general techniques and results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
