On sets of $n$ points in general position that determine lines that can be pierced by $n$ points

Chaya Keller; Rom Pinchasi

On sets of $n$ points in general position that determine lines that can be pierced by $n$ points

Combinatorics 2019-08-20 v1 Computational Geometry

Authors: Chaya Keller , Rom Pinchasi

Abstract

Let $P$ be a set of $n$ points in general position in the plane. Let $R$ be a set of $n$ points disjoint from $P$ such that for every $x,y \in P$ the line through $x$ and $y$ contains a point in $R$ outside of the segment delimited by $x$ and $y$ . We show that $P \cup R$ must be contained in a cubic curve.

Keywords

points in general position piercing lines cubic curve combinatorial geometry discrete geometry

Cite

@article{arxiv.1908.06390,
  title  = {On sets of $n$ points in general position that determine lines that can be pierced by $n$ points},
  author = {Chaya Keller and Rom Pinchasi},
  journal= {arXiv preprint arXiv:1908.06390},
  year   = {2019}
}

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9 pages, 5 figures

On sets of $n$ points in general position that determine lines that can be pierced by $n$ points

Abstract

Keywords

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