论文标题
连锁链，科赫链和点套装，带有许多三角形
Chains, Koch Chains, and Point Sets with many Triangulations
论文作者
论文摘要
我们介绍了一条链的抽象概念，该链是飞机上$ n $点的序列，按$ x $ - 坐标订购，因此就三角剖分而言，连续两个点之间的边缘是不可避免的。开发了链结构特性的一般理论，同时对它们的三角形数量有了一般的理解。 我们还描述了一种有趣的新型和具体的配置，由于它与Koch曲线的相似之处，我们称之为Koch链。然后，基于科赫连锁店的特定结构显示为$ω（9.08^n）$三角形。对于$ω（8.65^n）$的先前和长期下限，对于平面点集的最大三角数量，这是一个显着的改进。
We introduce the abstract notion of a chain, which is a sequence of $n$ points in the plane, ordered by $x$-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general theory of the structural properties of chains is developed, alongside a general understanding of their number of triangulations. We also describe an intriguing new and concrete configuration, which we call the Koch chain due to its similarities to the Koch curve. A specific construction based on Koch chains is then shown to have $Ω(9.08^n)$ triangulations. This is a significant improvement over the previous and long-standing lower bound of $Ω(8.65^n)$ for the maximum number of triangulations of planar point sets.
