Incidences with Curves in $\mathbb{R}^d$

Electronic Journal Of Combinatorics

Micha Sharir¹ 

关键词: Geometic incidences;    Discrete geometry;    Polynomial partitioning;    Polynomial curves;   

DOI  :  

学科分类：离散数学和组合数学

来源: Electronic Journal Of Combinatorics

【 摘 要 】

We prove that the number of incidences between $m$ points and $n$ bounded-degree curves with $k$ degrees of freedom in ${\mathbb R}^d$ is\[ O\left(m^{\frac{k}{dk-d+1}+\varepsilon}n^{\frac{dk-d}{dk-d+1}}+ \sum_{j=2}^{d-1} m^{\frac{k}{jk-j+1}+\varepsilon}n^

【 授权许可】

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