Proof of a conjecture by Walter Deuber concerning the distances between points of two types in \(R^d\)
type: Item
instance of: scholarly article
title: Proof of a conjecture by Walter Deuber concerning the distances between points of two types in \(R^d\)
zbMATH Open document ID: 0977.51010
DOI: 10.1016/S0012-365X(00)00209-0
published in: Discrete Mathematics
publication date: 2002-01-21T00:00:00Z
review text: The author proves Deuber's conjecture [Problem 303 in \textit{W. Deuber}, Discrete Math. 192, 348 (1998)]: For equal numbers of black and white points in Euclidean space the sum of the pairwise distances between points of equal colour is less than or equal to the sum of the pairwise distances between points of different colour, and equality holds only in the case when black and white points coincide. This is proved by simple counting and application of a well-known fact from integral geometry.
Mathematics Subject Classification ID: 51M99
Mathematics Subject Classification ID: 51K05
zbMATH DE Number: 1565950
Wikidata QID: Q122989900
author: Dietrich Morgenstern
reviewed by: Robert A. Gustafson
MaRDI profile type: Publication
full work available at URL: s0012-365x(00)00209-0
OpenAlex ID: W1987835555
description: scientific article; zbMATH DE number 1565950