Stabbing boxes with finitely many axis-parallel lines and flats - Chakraborty, Sutanoya; Ghosh, Arijit; Nandi, Soumi (arXiv.org, 2024)
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 \(0 ≤ k < d\). 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.