Homotheties and incidences
Abstract
We consider problems involving rich homotheties in a set S of n points in the plane
(that is, homotheties that map many points of S to other points of S). By reducing
these problems to incidence problems involving points and lines in R^3, we are able to
obtain refined and new bounds for the number of rich homotheties, and for the number
of distinct equivalence classes, under homotheties, of k-element subsets of S, for any
k ≥ 3. We also discuss the extensions of these problems to three and higher dimensions.
(that is, homotheties that map many points of S to other points of S). By reducing
these problems to incidence problems involving points and lines in R^3, we are able to
obtain refined and new bounds for the number of rich homotheties, and for the number
of distinct equivalence classes, under homotheties, of k-element subsets of S, for any
k ≥ 3. We also discuss the extensions of these problems to three and higher dimensions.
Research Areas
