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On the number of hinges defined by a point set in $mathbb R^2$ | Misha Rudnev
; | Date: |
15 Feb 2019 | Abstract: | This 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 | Services: | Forum | Review | PDF | Favorites |
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