Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902948 | Discrete Mathematics | 2017 | 7 Pages |
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 R3, 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 kâ¥3. We also discuss the extensions of these problems to three and higher dimensions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Dror Aiger, Micha Sharir,