Summary: Structural results for planar sets with many similar subsets
Bernardo M. Ábrego
California State University, Northridge. 2
Consider a k-element subset P of the plane. It is known that the maximum number of sets
similar to P that can be found among n points in the plane is (n2
) if and only if the cross
ratio of any quadruplet of points in P is algebraic , .
In this paper we study the structure of the extremal n-sets A which have cn2