Plane point sets with many squares or isosceles right triangles
Abstract
How many squares are spanned by n points in the plane? Here we study the corresponding maximum possible number S(n) of squares and determine the exact values for all n 17. For 18 n 100 we give lower bounds for S(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 14 and give lower bounds for 15 n 50.
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