Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (1): 46-58.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.004

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On the Number of F-Points Inside a Convex F-Polygon

  

  1. 1. Shijiazhuang No.1 Middle School, Shijiazhuang 050000, China; 2. College of Science, Hebei
    University of Science and Technology, Shijiazhuang 050018, China
  • Received:2022-08-25 Online:2024-03-30 Published:2024-03-13
  • Contact: WEI Xiang-lin (1974-), female, native of Zhangjiakou, Hebei, doctor, professor of Hebei University of Science and Technology, engages in combinatorial geometry and discrete geometry. E-mail: wxlhebtu@126.com
  • About author:GUO Zi-huan (1992-), female, native of Shijiazhuang, Hebei, master, lecturer of Shijiazhuang No.1 Middle School, engages in combinatorial geometry and discrete geometry; WEI Xiang-lin (1974-), female, native of Zhangjiakou, Hebei, doctor, professor of Hebei University of Science and Technology, engages in combinatorial geometry and discrete geometry.
  • Supported by:
     Supported by National Natural Science Foundation of China (Grant No. 12271139).

Abstract:

An F-polygon is a simple polygon whose vertices are F-points, which are
points of the set of vertices of a tiling of R2 by regular triangles and regular hexagons
of unit edge. Let f(v) denote the least possible number of F-points in the interior of a
convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,
f(12) = 12

Key words: Discrete geometry, F-polygon, Interior hull, Lattice polygon

CLC Number: