Minkowski addition of \(H\)-convex sets and related Helly-type theorems.
type: Item
instance of: scholarly article
title: Minkowski addition of \(H\)-convex sets and related Helly-type theorems.
zbMATH Open document ID: 1049.52001
DOI: 10.1016/S0097-3165(03)00101-8
published in: Journal of Combinatorial Theory. Series A
publication date: 2003-09-07T00:00:00Z
review text: Based on results on \(H\)-convex sets due to \textit{V. Boltyanski} and \textit{H. Martini} [J. Comb. Theory, Ser. A 93, No. 2, 292--309 (2001; Zbl 0976.52007)] and on the Minkowski addition of convex sets due to \textit{R. Schneider} [Convex bodies: The Brunn-Minkowski theory (Cambridge University Press, Cambridge) (1993; Zbl 0798.52001)], the authors prove a sufficient condition ensuring that the Minkowski sum of \(H\)-convex sets is itself an \(H\)-convex set. From this, using the method of \textit{L. Danzer}, \textit{B. Grünbaum} and \textit{V. Klee} [Proc. Sympos. Pure Math. 7, 101--180 (1963; Zbl 0132.17401)], they establish some theorems of Helly-type for \(H\)-convex sets.
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 1975838
zbMATH Keywords: \(H\)-convex set
zbMATH Keywords: non-one-sided
zbMATH Keywords: \(M\)-complete vector system
zbMATH Keywords: \(M\)-complete Minkowski sum
zbMATH Keywords: Minkowski difference
zbMATH Keywords: Helly-type theorems
author: V. G. Boltyanski
author: Horst Martini
MaRDI profile type: Publication
cites work: Q4110241
cites work: Carathéodory's theorem and \(H\)-convexity
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cites work: The Critical Set of a Convex Body
cites work: Q5287551
description: scientific article; zbMATH DE number 1975838