论文标题
抗兰斯理论问题，晶格点在多面有上，以及关于复曲面品种的杂货结构
Anti-Ramsey theory problems, lattice point counts on polytopes, and Hodge structures on the cohomology of toric varieties
论文作者
论文摘要
我们发现$ g $和子图$ h $的$ g $的家族$ g $的边缘颜色的数量避免了$ h $的单色颜色，这是由晶格点数或关于某种磨牙品种共同体的杂物结构确定的。通常，这给出了一类用几何结构的``反拉姆西理论问题''。例如，我们找到一个用于Ramsey数量的此类图形的数字。关键观察是，我们以前的结果以辅助简单复合物的$ h $ vextors表示，可以重新解释为避免了指定的禁忌子的单色颜色的辅助简单络合物的向量。专门针对由多面体三角剖分（例如单模型三角剖分）引起的简单络合物，我们获得了图形和禁止的亚图的家族，在这些家族中，避免了依赖于lattice点计数或hodge couties to toric cohomology of toric coleties of toric coleties of toric coleties of toric coleties的边缘色素避免了避免了禁止的子图的单色着色。
We find families of graphs $G$ and subgraphs $H$ of $G$ such that the number of edge colorings of $G$ avoiding a monochromatic coloring of $H$ is determined by lattice point counts or a Hodge structure on the cohomology of a certain toric variety. In general, this gives a class of ``anti-Ramsey theory problems'' with a geometric structure. For example, we find one for Ramsey numbers of classes of such graphs. The key observation is that our previous result expressing simplicial chromatic polynomials in terms of $h$-vectors of auxiliary simplicial complexes can be reinterpreted as one on edge colorings of graphs avoiding monochromatic colorings of specified forbidden subgraphs. Specializing to simplicial complexes arising from triangulations of polytopes (e.g. unimodular triangulations), we obtain families of graphs and forbidden subgraphs where edge colorings avoiding monochromatic colorings of the forbidden subgraphs depend on lattice point counts or Hodge structures on the cohomology of toric varieties.
