论离散几何中的可分离性

arXiv - MATH - Metric Geometry Pub Date : 2024-07-29 DOI:arxiv-2407.20169

Károly Bezdek, Zsolt Lángi

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引用次数: 0

摘要

Erd\H{o}s (Amer. Math. Monthly 52: 494-498, 1945) 的一个问题和 Fejes T\'oth and Fejes T\'oth (Acta Math. Acad. Sci. Hungar. 24: 229-232,1973)的一个理论开启了凸体不可分离排列的研究和凸体完全可分离堆积的研究，这两个课题都是从离散几何的角度分析可分性的概念。这篇文章回顾了在这些问题和一些密切相关的问题上取得的进展，并强调了尚未解决的相关问题。

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On separability in discrete geometry

A problem of Erd\H{o}s (Amer. Math. Monthly 52: 494-498, 1945) and a theorem of Fejes T\'oth and Fejes T\'oth (Acta Math. Acad. Sci. Hungar. 24: 229-232, 1973) initiated the study of non-separable arrangements of convex bodies and the investigation of totally separable packings of convex bodies with both topics analyzing the concept of separability from the point view of discrete geometry. This article surveys the progress made on these and some closely related problems and highlights the relevant questions that have been left open.

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arXiv - MATH - Metric Geometry

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