论文标题
关于多个共线三元组的点结构
On the structure of pointsets with many collinear triples
论文作者
论文摘要
猜想是，如果平面中的一组有限的点包含许多划线三元组，则该集合中有一些结构。我们将表明，在某些组合条件下，这些点包含三元组的特殊配置，证明了Elekes的猜想。使用证明中应用的技术，我们显示了Jamison定理的密度版本。如果凸位位置的几个点的许多点之间的不同方向数很小，则许多点在圆锥上。
It is conjectured that if a finite set of points in the plane contains many collinear triples then there is some structure in the set. We are going to show that under some combinatorial conditions such pointsets contain special configurations of triples, proving a case of Elekes' conjecture. Using the techniques applied in the proof we show a density version of Jamison's theorem. If the number of distinct directions between many pairs of points of a pointset in convex position is small, then many points are on a conic.
