The view-obstruction problem for 5-dimensional cubes
type: Item
instance of: scholarly article
title: The view-obstruction problem for 5-dimensional cubes
zbMATH Open document ID: 0936.11040
published in: Monatshefte für Mathematik
publication date: 1999-11-30T00:00:00Z
review text: The view obstruction problem for the \(n\)-cube is equivalent to the conjecture that, for any \(n\) positive integers \(v_1,\dots, v_n\), there is a real number \(x\) such that \(\|v_i x\|\geq (n+1)^{-1}\), \(i=1,\dots, n\). Here \(\|y\|\) denotes the distance from \(y\) to the nearest integer. The problem goes back to the reviewer (1968) and Cusick (1973), who also gave the useful geometric interpretation and various generalizations. Here he gives a lower bound for \(n=5\). The proof is based on methods by \textit{W. Bienia, L. Goddyn, P. Gvozdjak, A. Sebö} and \textit{M. Tarsi} [J. Comb. Theory, Ser. B 72, No. 1, 1-9 (1998; Zbl 0910.05064)].
reviewed by: Jörg M. Wills
Mathematics Subject Classification ID: 11J25
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 1300155
zbMATH Keywords: diophantine approximation
zbMATH Keywords: view obstruction
author: Thomas W. Cusick
MaRDI profile type: Publication
full work available at URL: s006050050033
OpenAlex ID: W2745568954
DOI: 10.1007/S006050050033
description: scientific article; zbMATH DE number 1300155