Stabbing boxes with finitely many axis-parallel lines and flats

08/21/2023

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by   Sutanoya Chakraborty, et al.

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We give necessary and sufficient condition for an infinite collection of axis-parallel boxes in 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.