凸F-多边形内部的F-点数

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

数学季刊 ›› 2024, Vol. 39 ›› Issue (1): 46-58.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.004

凸F-多边形内部的F-点数

郭自欢¹, 魏祥林²

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

收稿日期:2022-08-25 出版日期:2024-03-30 发布日期:2024-03-13
通讯作者: 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
作者简介: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.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 12271139).

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

GUO Zi-huan¹, WEI Xiang-lin²

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).

摘要/Abstract

摘要： 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

关键词: Discrete geometry, F-polygon, Interior hull, Lattice polygon

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

中图分类号:

O157.3

郭自欢, 魏祥林. 凸F-多边形内部的F-点数[J]. 数学季刊, 2024, 39(1): 46-58.

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.

[1]	魏祥林, 丁仁. 特定内点个数集合的存在性研究[J]. 数学季刊, 2012, 27(4): 606-614.
[2]	文家金, 柯睿, 吕涛. 含k-Brocard距离的一类几何不等式[J]. 数学季刊, 2006, 21(2): 210-219.

凸F-多边形内部的F-点数

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

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