Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (4): 606-614.

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A Note on the Existence of a Specified Number of Interior Points

  

  1. 1. College of Science, Hebei University of Science and Technology 2. College of Mathematics, Hebei Normal University

  • Received:2011-06-13 Online:2012-12-30 Published:2023-03-16
  • About author:WEI Xiang-lin(1974-), female, native of Zhangjiakou, Hebei, an associate professor of Hebei University of Science and Technology, engages in combinatorial geometry and discrete geometry; DING Ren(1939-), male, native of Yongkang, Zhejiang, a professor of Hebei Normal University, engages in combinatorial geometry and discrete geometry.
  • Supported by:
    Supported by the National Natural Science Foundation of China(10901045,11171088); Supported by the NSF of Hebei Province(A2010000828); Supported by the SF of Hebei University of Science and Technology(QD200955)

Abstract: An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k>1, let h(k) be the smallest integer such that every set of points in the plane, no three collinear, with at least h(k) interior points, has a subset of points with exactly k or k+1 interior points of P. We prove that h(5) = 11.


Key words: interior points, empty triangle, deficient point set, (x,y)-splitters

CLC Number: