A set of dual-extreme lattices
type: Item
instance of: scholarly article
title: A set of dual-extreme lattices
zbMATH Open document ID: 0889.11023
author: Jacques Martinet
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1998-03-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/230916
full work available at URL: jtnb9-1.html
review text: A lattice \(L\) in \(n\)-dimensional euclidean space is called dual-extreme if the geometric mean of the Hermite numbers of \(L\) and its dual \(L^*\) attains a local maximum. Following the classical method of Voronoi, \textit{A.-M. Bergé} and \textit{J. Martinet} [J. Number Theory 32, No. 1, 14-42 (1989; Zbl 0677.10022)] have characterized such lattices as being dual-perfect and dual-eutactic in the appropriate sense. As a consequence, if \(L\) is extreme and \(L^*\) is eutactic, then \(L\) is dual-extreme. However, for any even \(n\geq 8\), this paper gives an example where \(L\) is dual-extreme, neither \(L\) nor \(L^*\) is perfect, and only one of them is eutactic.
Mathematics Subject Classification ID: 11H55
Mathematics Subject Classification ID: 11H50
zbMATH DE Number: 1132892
zbMATH Keywords: extreme lattice
zbMATH Keywords: dual-extreme lattice
zbMATH Keywords: perfect lattice
zbMATH Keywords: eutactic lattice
reviewed by: Heinz-Georg Quebbemann
MaRDI profile type: Publication
OpenAlex ID: W1985257708
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DOI: 10.5802/JTNB.194
description: scientific article; zbMATH DE number 1132892