English

Homotheties and incidences

Computational Geometry 2017-09-12 v1

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.

Keywords

Cite

@article{arxiv.1709.02933,
  title  = {Homotheties and incidences},
  author = {Dror Aiger and Micha Sharir},
  journal= {arXiv preprint arXiv:1709.02933},
  year   = {2017}
}
R2 v1 2026-06-22T21:37:52.161Z