The local minima in the lattice-simplex covering problem
type: Item
instance of: scholarly article
zbMATH Open document ID: 1310.52021
author: Rod Forcade
author: H. Tracy Hall
author: W. Cocke
publication date: 2014-11-04T00:00:00Z
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 6365686
zbMATH Keywords: lattice covering
zbMATH Keywords: simplex
zbMATH Keywords: minimal density
zbMATH Keywords: local minimum
zbMATH Keywords: translates
zbMATH Keywords: algorithm
MaRDI profile type: Publication
title: The local minima in the lattice-simplex covering problem
published in: JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing
review text: The paper is devoted to coverings of the space \(\mathbb{R}^{n}\) with lattice translates of an \(n\)-simplex. The problem under investigation is to determine minimal density of such coverings.NEWLINENEWLINEFor the space \(\mathbb{R}^2\) the problem is completely solved. In the space \(\mathbb{Z}^3\) a local minimum corresponding to the 84-shape was found independently by several authors using computer search (for the simplex which is the convex hull of the unit basis vectors).NEWLINENEWLINEIn the present paper, the authors define the concept of combinatorial type and propose a search algorithm which determines the local minima within an arbitrary combinatorial type.
reviewed by: Elizaveta Zamorzaeva
description: scientific article; zbMATH DE number 6365686