论文标题
超图提图的代数特性
Algebraic Properties of a Hypergraph Lifting Map
论文作者
论文摘要
Hypergraph Ramsey理论的最新工作涉及引入“提升图”，该图像将一定的$ 3 $均匀的超图与给定图相关联，以可预测的方式界定了集团。在本文中，我们将起重图解释为线性变换。这种解释使我们能够使用代数技术证明了起重地图的几种结构属性，最终以某些$ 3 $均匀的超刻刻度Ramsey数字达到新的下限。
Recent work in hypergraph Ramsey theory has involved the introduction of a "lifting map" that associates a certain $3$-uniform hypergraph to a given graph, bounding cliques in a predictable way. In this paper, we interpret the lifting map as a linear transformation. This interpretation allows us to use algebraic techniques to prove several structural properties of the lifting map, culminating in new lower bounds for certain $3$-uniform hypergraph Ramsey numbers.
