具有无限Cop数的紧度量空间。

IF 0.6 3区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Discrete & Computational Geometry Pub Date : 2025-01-01 Epub Date: 2024-10-14 DOI:10.1007/s00454-024-00696-0

Agelos Georgakopoulos

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引用次数: 0

摘要

Mohar最近将经典的“警察和强盗”游戏从图形改编为度量空间，从而统一了先前研究的追捕-逃避游戏。他推测在任何紧致测地线度量空间上都可以有有限个条子，并且当空间是一个简单伪流形时，它们的数目可以根据同调群的秩上界。我们通过构造一个具有无限cop数的s3上的度量来反驳这些猜想。提出的问题比解决的问题多。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Compact Metric Spaces with Infinite Cop Number.

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Compact Metric Spaces with Infinite Cop Number.

Mohar recently adapted the classical game of Cops and Robber from graphs to metric spaces, thereby unifying previously studied pursuit-evasion games. He conjectured that finitely many cops can win on any compact geodesic metric space, and that their number can be upper-bounded in terms of the ranks of the homology groups when the space is a simplicial pseudo-manifold. We disprove these conjectures by constructing a metric on $S^{3}$ with infinite cop number. More problems are raised than settled.

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来源期刊

Discrete & Computational Geometry 数学-计算机：理论方法

CiteScore

1.80

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.