Stabbing boxes with finitely many axis-parallel lines and flats
In this short note, we provide the necessary and sufficient condition for an infinite collection of axis-parallel boxes in \(\mathbb{R}^{d}\) to be pierceable by finitely many axis-parallel \(k\)-flats, where \(0 \leq k < d\). We also consider colorful generalizations of the above result and esta...
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| Vydané v: | arXiv.org |
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| Hlavní autori: | , , |
| Médium: | Paper |
| Jazyk: | English |
| Vydavateľské údaje: |
Ithaca
Cornell University Library, arXiv.org
11.12.2024
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| Predmet: | |
| ISSN: | 2331-8422 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | In this short note, we provide the necessary and sufficient condition for an infinite collection of axis-parallel boxes in \(\mathbb{R}^{d}\) to be pierceable by finitely many axis-parallel \(k\)-flats, where \(0 \leq k < d\). We also consider colorful generalizations of the above result and establish their feasibility. The problem considered in this paper is an infinite variant of the Hadwiger-Debrunner \((p, q)\)-problem. |
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| Bibliografia: | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.2308.10479 |