New Helly-type results for discrete boxes: Quantitative colorful and $(p,q)$-variants

Rahul Gangopadhyay, Alexander Polyanskii, Wei Rao

In 2008, Halman showed that for any finite set $P\subset {\mathbb{R}}^d$ and any finite family $\mathcal{B}$ of axis-parallel boxes in ${\mathbb{R}}^d$, if the intersection of $P$ and a…