On the number of unit-area triangles spanned by convex grids in the plane

Orit E. Raz*, Micha Sharir, Ilya D. Shkredov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A finite set of real numbers is called convex if the differences between consecutive elements form a strictly increasing sequence. We show that, for any pair of convex sets A,B⊂R, each of size n1/2, the convex grid A×B spans at most O(n37/17log2/17⁡n) unit-area triangles. Our analysis also applies to more general families of sets A, B, known as sets of Szemerédi–Trotter type.

Original languageAmerican English
Pages (from-to)25-33
Number of pages9
JournalComputational Geometry: Theory and Applications
Volume62
DOIs
StatePublished - 1 Apr 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

  • Cobinatorial geometry
  • Convex sets
  • Repeated Configurations

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