On Lines and Joints

On Lines and Joints (2009)

by Haim Kaplan , Micha Sharir , Eugenii Shustin

Citations:

2 - 0 self

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Datum	Value	Source
TITLE	On Lines and Joints	user correction
AUTHOR NAME	Haim Kaplan	user correction
AUTHOR ADDR	School of Computer Science, Tel Aviv University, Tel Aviv 69978 Israel;	user correction
AUTHOR NAME	Micha Sharir	user correction
AUTHOR ADDR	School of Computer Science, Tel Aviv University, Tel Aviv 69978 Israel;	user correction
AUTHOR NAME	Eugenii Shustin	user correction
AUTHOR ADDR	School of Computer Science, Tel Aviv University, Tel Aviv 69978 Israel;	user correction
ABSTRACT	Let L be a set of n lines in R d, for d ≥ 3. A joint of L is a point incident to at least d lines of L, not all in a common hyperplane. Using a very simple algebraic proof technique, we show that the maximum possible number of joints of L is Θ(n d/(d−1)). For d = 3, this is a considerable simplification of the orignal algebraic proof of Guth and Katz [9], and of the follow-up simpler proof of Elekes et al. [6]. Some extensions, e.g., to the case of joints of algebraic curves, are also presented.	user correction
YEAR	2009	SVM HeaderParse 0.2
CITATIONS	12 found	ParsCit 1.0