论文标题
具有无限许多极端结构的超图
Hypergraphs with infinitely many extremal constructions
论文作者
论文摘要
我们给出了第一个精确的稳定性结果，即Hypergraphturán问题，无限的许多极端结构在编辑距离上彼此遥远。这包括一个带有Turán密度$ 2/9 $的三重系统的示例，从而回答了第三和第四作者提出的一些问题，并介绍了有关可行的HyperGraphs区域。我们的结果还提供了极端结构，其阴影密度是先验数字。 我们的新方法是构建某些多项式多项式，这些多项式可以在线段上获得其最大值（在标准单纯段），然后使用这些多项式来定义具有极端构造的超图上的操作。
We give the first exact and stability results for a hypergraph Turán problem with infinitely many extremal constructions that are far from each other in edit-distance. This includes an example of triple systems with Turán density $2/9$, thus answering some questions posed by the third and fourth authors and Reiher about the feasible region of hypergraphs. Our results also provide extremal constructions whose shadow density is a transcendental number. Our novel approach is to construct certain multilinear polynomials that attain their maximum (in the standard simplex) on a line segment and then to use these polynomials to define an operation on hypergraphs that gives extremal constructions.
