Plane point sets with many squares or isosceles right triangles

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Kurz, Sascha:
Plane point sets with many squares or isosceles right triangles.
Bayreuth , 2021 . - 31 S.

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Abstract

How many squares are spanned by n points in the plane? Here we study the corresponding maximum possible number of squares and determine the exact values for all n≤17. For 18≤n≤100$ we give corresponding lower bounds. 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≤14 and give lower bounds for 15≤n≤50.