二维空间中给定顶点范数集凸形的不存在性

IF 1.4 4区数学 Q1 MATHEMATICS Carpathian Journal of Mathematics Pub Date : 2022-12-21 DOI:10.37193/cjm.2023.02.11

Kirati Sriamorn, S. Sriswasdi, Supanut Chaidee

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引用次数: 0

摘要

给定一组顶点范数，或距原点的距离，在二维空间中，并不总是存在其顶点满足顶点范数的凸配置或凸多边形。在这项研究中，我们基于多边形围绕原点的角度，提供了这种凸配置存在的充要条件。给出了构造满足给定顶点范数集的凸配置的一般策略，以及不存在这种凸配置的顶点范数集实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Non-Existence of Convex Configuration for a Given Set of Vertex-Norm in Two-Dimensional Space

Given a set of vertex-norm, or distances from the origin, in two-dimensional space, there does not always exist a convex configuration, or convex polygon, whose vertices satisfy the vertex-norm. In this research, we provide the necessary and sufficient conditions, based on the angles spanned by the polygon around the origin, for the existence of such convex configuration. General strategies for constructing a convex configuration satisfying a given vertex-norm set as well as examples of vertex-norm sets for which no such convex configuration exists are also illustrated.

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来源期刊

Carpathian Journal of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.