平面网格点中无直角的最大点集构造

Construction of Maximum Points Set without Right Angles about Square Lattice Points in the Plane

本文首先介绍了关于点集中无直角的最大点集的研究现状;然后讨论了在二维平面上m×n网格点中无直角的最大点集的构造,通过利用坐标投影法和代数法,分别证明得到此最大点集的基数为m+n-2;最后给出一些关于二维平面网格点中有待解决的新问题.

In this paper, the research status of maximum points set without right angles on a points set is introduced. Then, the construction of the largest points set without right angles about an m × n square lattice points in the 2-dimensional plane is discussed. By using the coordinate projection method and the algebraic method, it is shown that the cardinality of the largest points set is rn ＋ n - 2. Finally, some new problems to be solved on the square lattice points in the 2-dimensional plane are given.