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arXiv · 2112.12716

Plane point sets with many squares or isosceles right triangles

Sascha Kurz
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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 $15\le n\le 50$.

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Sascha Kurz. 2021-12-23. Plane point sets with many squares or isosceles right triangles. https://arxiv.org/abs/2112.12716

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