On partition of special 3-dimensional polyhedrons into \(d\)-convex parts
type: Item
instance of: scholarly article
zbMATH Open document ID: 0996.52008
author: Ion Băţ
publication date: 2002-11-04T00:00:00Z
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 52B70
zbMATH DE Number: 1663585
zbMATH Keywords: \(d\)-convexity
zbMATH Keywords: subdivisions by parallelepipeds
zbMATH Keywords: containerization problem
MaRDI profile type: Publication
title: On partition of special 3-dimensional polyhedrons into \(d\)-convex parts
published in: Anale Ştiinţifice Facultatea de Matematică şi Informatică. Universitatea de Stat din Moldova
review text: A subset \(M\) of a space with metric \(d\) is called \(d\)-convex if every \(d\)-segment with endpoints in \(M\) is contained in \(M\); here, a \(d\)-segment with endpoints \(a\) and \(b\) consists of all points \(x\) such that \(d(a,x)+ d(x,b)= d(a,b)\). The author considers real 3-space \(\mathbb{E}^3\) equipped with the metric \(d\) associated with the norm \(\|x\|=|x_1|+|x_2|+|x_3|\). In this space, a compact \(d\)-convex body is necessarily a parallelepiped with edges parallel to the coordinate axes.NEWLINENEWLINENEWLINEFor certain types of polyhedra \(P\) in \(\mathbb{E}^3\), the author obtains an explicit formula for the smallest number of \(d\)-convex parts (parallelepipeds with edges parallel to the coordinate axes) into which \(P\) can be partitioned. The polyhedra \(P\) are handlebodies, or handlebodies with holes, and they have their edges parallel to the coordinate axes.
reviewed by: Egon Schulte
description: scientific article; zbMATH DE number 1663585