图同态的理想
Ideals of Graph Homomorphisms
摘要：
在组合交换代数和代数统计中，许多环面理想都是由图构造的。考虑到图的范畴结构，我们给以前的结果一个更函的背景下，并推广它们通过引入理想的图同态。对于这类新的理想，我们研究如何图的拓扑影响的代数性质。我们描述了明确的Grobner基地的几个类，推广结果Hibi，Sturmfels和Sullivant。我们的主要工具之一是复曲面纤维积，我们采用Engstrom、Kahle和Sullivant的结果。由我们的理想定义的格多面体包括优化理论中的重要类，如独立集多面体。
英文摘要：
In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by introducing the ideals of graph homomorphisms. For this new class of ideals we investigate how the topology of the graphs influence the algebraic properties. We describe explicit Grobner bases for several classes, generalizing results by Hibi, Sturmfels and Sullivant. One of our main tools is the toric fiber product, and we employ results by Engstrom, Kahle and Sullivant. The lattice polytopes defined by our ideals include important classes in optimization theory, as the stable set polytopes.
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