Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane

Károly J. Böröczky, M. Matolcsi, I. Ruzsa, Francisco Santos, Oriol Serra

Research output: Contribution to journalArticle

Abstract

For a set A of points in the plane, not all collinear, we denote by tr (A) the number of triangles in a triangulation of A, that is, tr (A) = 2 i+ b- 2 , where b and i are the numbers of boundary and interior points of the convex hull [A] of A respectively. We conjecture the following discrete analog of the Brunn–Minkowski inequality: for any two finite point sets A, B⊂ R2 one has tr(A+B)≥tr(A)1/2+tr(B)1/2.We prove this conjecture in the cases where [ A] = [ B] , B= A∪ { b} ,

Original languageEnglish
JournalDiscrete and Computational Geometry
DOIs
Publication statusAccepted/In press - Jan 1 2019

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Brunn-Minkowski Inequality
Minkowski Sum
Interior Point
Triangulation
Collinear
Convex Hull
Point Sets
Finite Set
Triangle
Industry
Denote
Analogue
Generalization
Business

Keywords

  • Brunn–Minkowski theory
  • Minkowski sum
  • Triangulations

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane. / Böröczky, Károly J.; Matolcsi, M.; Ruzsa, I.; Santos, Francisco; Serra, Oriol.

In: Discrete and Computational Geometry, 01.01.2019.

Research output: Contribution to journalArticle

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