Refinement of the lower bound for the index in the octahedron problem
type: Item
instance of: scholarly article
title: Refinement of the lower bound for the index in the octahedron problem
zbMATH Open document ID: 0876.11028
author: Yanyan Li
published in: Moscow University Mathematics Bulletin
publication date: 1996-03-27T00:00:00Z
review text: In this paper the author gives a lower bound for the index in the octahedron problem. He proves that the maximum index \(I\) defined by the index of the sublattice \(\Lambda'\) of \(\Lambda\) spanned by a set of linearly independent vector systems giving an admissible octahedron of \(\Lambda\) is greater than \[ {n! \over 2^{n-1}} \bigl(1+(2+ \delta)^{-n} \bigr), \] for sufficiently large \(n\) (here \(\delta>0\) is an arbitrarily small number). The method of the proof uses an averaging procedure which naturally appears in such problems.
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 848927
zbMATH Keywords: lower bound for the index
zbMATH Keywords: octahedron problem
reviewed by: Ákos G. Horváth
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 848927