On lattice dicing
type: Item
instance of: scholarly article
title: On lattice dicing
zbMATH Open document ID: 0809.52019
author: S. S. Ryshkov
author: R. M. Erdahl
published in: European Journal of Combinatorics
publication date: 1995-03-29T00:00:00Z
review text: A lattice dicing is a finite set \(\{G_ 1, \dots, G_ r\}\) of \(D\)- families of parallel hyperplanes in \(\mathbb{R}^ n\) which is both non- degenerate and vertex-regular, where the three needed terms are correspondingly defined as follows: A \(d\)-family contains an infinite number of equispaced parallel hyperplanes ``extending in both directions'', and the system \(\{G_ 1, \dots, G_ r\}\) is non- degenerate if it contains \(n\) \(D\)-families with linearly independent normal vectors; for the vertex-regularity we demand that each vertex of the dicing is contained in one hyperplane from each of the \(D\)-families. The authors investigate the relations of lattice dicings to the geometry of numbers, and they give a complete description of the possible lattice dicings in \(\mathbb{R}^ n\) with \(n \leq 5\).
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 11H99
zbMATH DE Number: 683268
zbMATH Keywords: arrangements of hyperplanes
zbMATH Keywords: lattice dicing
zbMATH Keywords: geometry of numbers
MaRDI profile type: Publication
full work available at URL: eujc.1994.1049
OpenAlex ID: W2095168501
DOI: 10.1006/EUJC.1994.1049
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description: scientific article; zbMATH DE number 683268