Stabbing boxes with finitely many axis-parallel lines and flats

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 esta...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org
Hauptverfasser:	Chakraborty, Sutanoya, Ghosh, Arijit, Nandi, Soumi
Format:	Paper
Sprache:	Englisch
Veröffentlicht:	Ithaca Cornell University Library, arXiv.org 11.12.2024
Schlagworte:	Boxes
ISSN:	2331-8422
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	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.
Bibliographie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2308.10479