Plane point sets with many squares or isosceles right triangles

Sascha Kurz

Plane point sets with many squares or isosceles right triangles

Combinatorics 2021-12-24 v1 Metric Geometry

Authors: Sascha Kurz

Abstract

How many squares are spanned by $n$ points in the plane? Here we study the corresponding maximum possible number $S_{\square}(n)$ of squares and determine the exact values for all $n\le 17$ . For $18\le n\le 100$ we give lower bounds for $S_{\square}(n)$ . Besides that a few preliminary structural results are obtained. For the related problem of the maximum possible number of isosceles right triangles we determine the exact values for $n\le 14$ and give lower bounds for $15\le n\le 50$ .

Keywords

incidence geometry of points and lines triangulations

Cite

@article{arxiv.2112.12716,
  title  = {Plane point sets with many squares or isosceles right triangles},
  author = {Sascha Kurz},
  journal= {arXiv preprint arXiv:2112.12716},
  year   = {2021}
}

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31 pages, 9 tables, 10 figures

Plane point sets with many squares or isosceles right triangles

Abstract

Keywords

Cite

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