2 research outputs found
Stabbing boxes with finitely many axis-parallel lines and flats
We give necessary and sufficient condition for an infinite collection of
axis-parallel boxes in to be pierceable by finitely many
axis-parallel -flats, where . 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 -problem.Comment: 13 page
Dimension Independent Helly Theorem for Lines and Flats
We give a generalization of dimension independent Helly Theorem of
Adiprasito, B\'{a}r\'{a}ny, Mustafa, and Terpai (Discrete & Computational
Geometry 2022) to higher dimensional transversal. We also prove some
impossibility results that establish the tightness of our extension.Comment: 10 page