论文标题
点线入射构建体的常数
The constant of point-line incidence constructions
论文作者
论文摘要
我们研究了Szemerédi-Trotter定理常数的下限。特别是，我们表明，最新的无限分类配置家族满足$ i（{\ Mathcal p}，{\ Mathcal l}）\ ge（c+o（1））| {\ Mathcal P} |^{2/3} | {\ Mathcal L} | {\ Mathcal L} |^2/3} $ cobl我们的技术是基于研究Euler基本功能的各种属性。我们还将Elekes构造的当前最佳常量从1提高到约1.27。从说明性的角度来看，这是对ERD \ H OS结构常数的首次完整分析。
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 $I({\mathcal P},{\mathcal L})\ge (c+o(1)) |{\mathcal P}|^{2/3}|{\mathcal L}|^{2/3}$, 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 Erd\H os's construction.
