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 (9.08ⁿ) triangulations. This is a significant improvement over the previous and long-standing lower bound of Ω (8.65ⁿ) for the maximum number of triangulations of planar point sets.

我们引入了链的抽象概念，它是平面上的n 个点的序列，按x坐标排序，因此就三角测量而言，任何两个连续点之间的边是不可避免的。发展了链的结构特性的一般理论，以及对它们的三角剖分数量的一般理解。

我们还描述了一个有趣的新的具体配置，我们将其称为科赫链，因为它与科赫曲线相似。然后显示基于 Koch 链的特定构造具有 Ω (9.08 ⁿ ) 三角剖分。对于平面点集的最大三角剖分数量，这是对之前和长期存在的 Ω (8.65 ^{n ) 下界的显着改进。}