Tiling, packing, and covering by clusters
type: Item
instance of: scholarly article
title: Tiling, packing, and covering by clusters
zbMATH Open document ID: 0603.52007
DOI: 10.1216/RMJ-1986-16-2-277
author: Sherman Stein
published in: Rocky Mountain Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: This long paper represents a very nice and attractive survey in the theory of tiling, packing and covering by clusters. Recall that a cluster is a union of a finite number of cubes from the standard lattice of cubes. The author presents mainly the results of Everett, Galovich, Hamaker, Hickerson, Loomis, Newman, Stein and Szabo. The paper contains six sections: Clusters, The cross and semicross, Multiplier sets, The multiplier set \(\{\) 1,2,...,k\(\}\), The multiplier set \(\{\pm 1,\pm 2,...,\pm k\}\), Origins. Each section is divided into two or three subsections and contains many important notions and results in this field. There are also many open questions and results that suggest lines of further investigation. A rich and suggestive bibliography in this field is given.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 3973731
zbMATH Keywords: star body
zbMATH Keywords: survey
zbMATH Keywords: tiling, packing and covering by clusters
zbMATH Keywords: cross
zbMATH Keywords: semicross
zbMATH Keywords: Multiplier sets
zbMATH Keywords: bibliography
reviewed by: Dorin Andrica
MaRDI profile type: Publication
full work available at URL: rmj-1986-16-2-277
OpenAlex ID: W2028215291
description: scientific article; zbMATH DE number 3973731