Stabbing boxes with finitely many axis-parallel lines and flats
| Autor: | Chakraborty, Sutanoya, Ghosh, Arijit, Nandi, Soumi |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Discrete Mathematics, 348(2): 114269, 2025 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.disc.2024.114269 |
| Popis: | 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. Comment: 17 pages and 2 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|