Maximum number of points in general position in a random subset of finite 3-dimensional spaces

IF 0.7 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2026-07-01 Epub Date: 2026-01-14 DOI:10.1016/j.comgeo.2026.102244

József Balogh , Haoran Luo

引用次数: 0

Abstract

Let

α (F_{q}^{d}, p)

be the maximum possible size of a point set in general position in the p-random subset of

F_{q}^{d}

. In this note, we determine the order of magnitude of

α (F_{q}^{3}, p)

up to a polylogarithmic factor by proving a balanced supersaturation result for the sets of 4 points in the same plane.

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有限三维空间的随机子集中一般位置上的最大点数

设α(Fqd,p)为Fqd的p-随机子集中一般位置上的点集的最大可能大小。在本注中，我们通过证明同一平面上4个点的集合的平衡过饱和结果来确定α(Fq3,p)直至多对数因子的数量级。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.