Stabbing boxes with finitely many axis-parallel lines and flats
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910741063270400 |
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| author | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| author_facet | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_10479 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stabbing boxes with finitely many axis-parallel lines and flats Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi Combinatorics Computational Geometry 52A35 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. |
| title | Stabbing boxes with finitely many axis-parallel lines and flats |
| topic | Combinatorics Computational Geometry 52A35 |
| url | https://arxiv.org/abs/2308.10479 |