点-线关联构造的常数

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-10-01 DOI:10.1016/j.comgeo.2023.102009

Martin Balko , Adam Sheffer , Ruiwen Tang

引用次数: 1

摘要

我们研究了Szemerédi–Trotter定理常数的一个下界。特别地，我们证明了最近的无穷一族点线配置满足I（P，L）≥（c+o（1））|P|2/3|L|2/3，其中c≈1.27。我们的技术是基于对欧拉瞬变函数的各种性质的研究。我们还将Elekes结构的当前最佳常数从1提高到约1.27。从阐释的角度来看，这是第一次全面分析埃尔德斯结构的常数。

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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The constant of point–line incidence constructions

We study a lower bound for the constant of the Szemerédi–Trotter theorem. In particular, we show that a recent infinite family of point-line configurations satisfies $I (P, L) \geq (c + o (1)) | P |^{2 / 3} | L |^{2 / 3}$ , with $c \approx 1.27$ . Our technique is based on studying a variety of properties of Euler's totient function. We also improve the current best constant for Elekes's construction from 1 to about 1.27. From an expository perspective, this is the first full analysis of the constant of Erdős's construction.

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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.