Homotheties and incidences

Dror Aiger*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 k≥3. We also discuss the extensions of these problems to three and higher dimensions.

Original languageEnglish
Pages (from-to)2011-2017
Number of pages7
JournalDiscrete Mathematics
Issue number7
StatePublished - Jul 2018


FundersFunder number
Israel Science Fund
Israeli Centers for Research Excellence4/11
Blavatnik Research Fund in Computer Science
Tel Aviv University


    • Combinatorial geometry
    • Homothety transformation
    • Incidences


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