The view-obstruction problem for \(n\)-dimensional cubes
type: Item
instance of: scholarly article
title: The view-obstruction problem for \(n\)-dimensional cubes
zbMATH Open document ID: 0921.11030
published in: Journal of Number Theory
publication date: 1999-03-30T00:00:00Z
review text: The view-obstruction problem for the \(n\)-dimensional cube is equivalent to the conjecture that for any \(n\) positive integers \(v_1,\dots, v_n\) there is a real number \(x\) with \[ \| v_ix\|\geq (n+1)^{-1}, \quad i=1,\dots, n, \] where \(\| y\|\) denotes the distance from \(y\) to the next integer. This conjecture has been previously solved for \(n=4\). The authors prove for \(p=2n-3\) prime and \(n\geq 4\) that there is a real \(x\) with \(\| v_ix\|\geq p^{-1}\), \(i=1,\dots, n\). Some further related results are given.
reviewed by: Jörg M. Wills
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 52C10
Mathematics Subject Classification ID: 11J13
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 1271769
zbMATH Keywords: packings
zbMATH Keywords: Erdős problems
zbMATH Keywords: view-obstruction problem
author: Yonggao Chen
author: Thomas W. Cusick
MaRDI profile type: Publication
full work available at URL: jnth.1998.2309
OpenAlex ID: W2051900231
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DOI: 10.1006/JNTH.1998.2309
description: scientific article; zbMATH DE number 1271769