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29 March 2024
 
  » arxiv » 1902.5791

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On the number of hinges defined by a point set in $mathbb R^2$
Misha Rudnev ;
Date 15 Feb 2019
AbstractThis note strengthens, modulo a $log n$ factor, the Guth-Katz estimate for the number of pair-wise incidences of lines in $mathbb R^3$, arising in the context of the plane Erd"os distinct distance problem to a second moment bound. This enables one to show that the number of distinct types of three-point hinges, defined by a plane set of $n$ points is $gg n^2log^{-3} n$, where a hinge is identified by fixing two pair-wise distances in a point triple.
Source arXiv, 1902.5791
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