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

GUO Zi-huan, WEI Xiang-lin

doi:10.13371/j.cnki.chin.q.j.m.2024.01.004

Chinese Quarterly Journal of Mathematics >

2024 , Vol. 39 >Issue 1: 46 - 58

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.01.004

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

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1. Shijiazhuang No.1 Middle School, Shijiazhuang 050000, China; 2. College of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China

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.

Received date: 2022-08-25

Online published: 2024-03-13

Supported by

Supported by National Natural Science Foundation of China (Grant No. 12271139).

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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

Cite this article

GUO Zi-huan, WEI Xiang-lin . On the Number of F-Points Inside a Convex F-Polygon[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(1) : 46 -58 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.004

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