The defect of an admissible octahedron in a lattice
type: Item
instance of: scholarly article
title: The defect of an admissible octahedron in a lattice
zbMATH Open document ID: 0855.52005
DOI: 10.1007/BF02305095
author: Yanyan Li
published in: Mathematical Notes
publication date: 1997-02-16T00:00:00Z
review text: Let \(\Lambda\) be a lattice in euclidean \(n\)-space \(\mathbb{R}^n\), let \(e_1, \dots, e_n \in \Lambda\) be linear independent vectors, and let \(f\) be the maximal number of vectors in a set \(\{e_{i_1}, \dots, e_{i_f}\}\), that may be complemented to a basis of \(\Lambda \). The difference \(n - f\) is called the defect, and the author discusses various properties (e.g. asymptotic) of the defect.
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 898962
zbMATH Keywords: euclidean \(n\)-space
zbMATH Keywords: lattice
zbMATH Keywords: maximal number of vectors
zbMATH Keywords: defect
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: On sums of powers of linear forms. I
cites work: A new upper bound to the minimum value of the sum of linear homogeneous forms
cites work: An Introduction to the Geometry of Numbers
cites work: Q3751649
cites work: SOME PROBLEMS IN THE THEORY OF DIOPHANTINE APPROXIMATION
cites work: Lattice Octahedra and Sums of Powers of Linear Forms
cites work: Refinement of the lower bound for the index in the octahedron problem
cites work: Lattice Octahedra
cites work: Le "Problème des Octaèdres" en dimension 5
full work available at URL: https://doi.org/10.1007/bf02305095
OpenAlex ID: W2019833539
description: scientific article; zbMATH DE number 898962