The set of neighbours of a set in a point-lattice
type: Item
instance of: scholarly article
title: The set of neighbours of a set in a point-lattice
zbMATH Open document ID: 0810.52012
DOI: 10.1016/0012-365X(94)90032-9
published in: Discrete Mathematics
publication date: 1994-11-03T00:00:00Z
review text: For a lattice \(\Lambda \subset \mathbb{R}^ n\) and a bounded \(A \subset \mathbb{R}^ n\) the set \(S(A) = \{u \in \Lambda \mid A \cap (A + u) \neq \emptyset\}\) is called the set of neighbours of \(A\) in \(\Lambda\). Further \(N(A) = \text{card } S(A)\) is the number of neighbours (`Nachbarnzahl'), introduced by Hadwiger. The author improves lower bounds for \(N(A)\), given by Erdős, Rogers and Groemer.
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 681704
zbMATH Keywords: point-lattice
zbMATH Keywords: number of neighbours
author: Béla Uhrin
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: An Introduction to the Geometry of Numbers
cites work: Q3992416
cites work: Über Treffanzahlen in Figurengittern
cites work: Q3751649
cites work: Überdeckung des Raumes durch translationsgleiche Punktmengen und Nachbarnzahl
cites work: Q3996431
cites work: Some estimations useful in geometry of numbers
cites work: A remark to the paper of H. Hadwiger: ``Überdeckung des Raumes durch translationsgleiche Punktmengen und Nachbarnzahl''
cites work: Q4723977
cites work: Q3833149
cites work: Q4328210
cites work: A description of the segment \([1,T]\), where \(T\) is the meeting number of a set-lattice
cites work: Q4714565
description: scientific article; zbMATH DE number 681704