On lines and Joints

2009/06/02 by Kaplan, Haim, Sharir, Micha, Shustin, Eugenii · 1 citation
#Computational Geometry (cs.CG) #FOS: Computer and information sciences #I.3.5

paper · doi:10.48550/arxiv.0906.0558

Abstract

Let L be a set of n lines in \reals^d, for d≥ 3. A \em 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~\citeGK, and of the follow-up simpler proof of Elekes et al. \citeEKS.

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