单位正方形和单位圆盘的不透明集合的显式下界

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2026-05-13 DOI:10.1007/s10474-026-01606-x

Markus Kiderlen, Florian Pausinger

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引用次数: 0

摘要

导出了欧几里得平面上单位圆盘和单位正方形的最短不透明集长度的显式下界。结果是基于Kawamura， Moriyama， Otachi和Pach[9]的一般方法的明确应用。利用Steinerberger最近对长度接近Jones界的直障的可能方向的观察，我们将[9]中的界提高了3倍以上。单位圆盘的势垒界是基于基于[9]的一般方法中的自由参数可以由于圆盘的强对称性而得到优化的思想而提出的。我们的方法说明了该方法的力量和局限性。

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Explicit lower bounds for opaque sets of unit square and unit disc

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Explicit lower bounds for opaque sets of unit square and unit disc

Explicit lower bounds for the length of the shortest opaque set for the unit disc and the unit square in the Euclidean plane are derived. The results are based on an explicit application of the general method of Kawamura, Moriyama, Otachi and Pach [9]. Employing a recent observation by Steinerberger on the possible orientations of straight barriers with length close to Jones’ bound, we improve the bound in [9] by more than a factor 3. The bound for barriers of the unit disc is new and based on the idea that the free parameters in the general method from [9] can be optimized due to the strong symmetry properties of the disc. Our approach illustrates both the power and the limitations of the method.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.