Translator Disclaimer
may 2022 Colorful Carathéodory, Helly and Sierksma numbers of convexity spaces
Krzysztof Kołodziejczyk
Bull. Belg. Math. Soc. Simon Stevin 28(4): 513-529 (may 2022). DOI: 10.36045/j.bbms.210414

Abstract

Since the appearance of the so-called colorful Carathéodory and Helly theorems in $\mathbb{R}^d$, many papers have been published with colorful generalizations of classical results in combinatorial geometry. The growing number of such publications is a good motivation to consider colorful analogs of known results in a more abstract setting. This is why we introduce in this note the colorful Carathéodory, Helly and Sierksma numbers of a convexity space. We study relationships between these new numbers and the classical (monochromatic) Carathéodory, Helly and exchange numbers of convexity spaces. Special attention is paid to the new numbers in product convexity and convex sum spaces.

Citation

Download Citation

Krzysztof Kołodziejczyk. "Colorful Carathéodory, Helly and Sierksma numbers of convexity spaces." Bull. Belg. Math. Soc. Simon Stevin 28 (4) 513 - 529, may 2022. https://doi.org/10.36045/j.bbms.210414

Information

Published: may 2022
First available in Project Euclid: 11 May 2022

Digital Object Identifier: 10.36045/j.bbms.210414

Subjects:
Primary: 52A01 , 52A35

Keywords: Carathéodory number , colorful Carathéodory and Helly theorems , convexity space , exchange number , Helly number

Rights: Copyright © 2022 The Belgian Mathematical Society

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.28 • No. 4 • may 2022
Back to Top