A vector-sum theorem in two-dimensional space
type: Item
instance of: scholarly article
title: A vector-sum theorem in two-dimensional space
zbMATH Open document ID: 0579.52005
DOI: 10.1007/BF01857593
published in: Periodica Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: In the spirit of a classical reordering theorem by Steinitz, the authors construct a number \(C\leq 18\) such that every finite set \(X\subset [- 1,1]\times [-1,1]\) with sum zero can be ordered such that the sum of the first k elements belongs to the rectangle [-1,1]\(\times [-C,C]\), for every k. The proof gives an O((card X)\({}^ 2)\) algorithm to obtain such an ordering of X.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 52-04
Mathematics Subject Classification ID: 90B35
zbMATH DE Number: 3927800
zbMATH Keywords: scheduling theory
zbMATH Keywords: bounded partial sums
zbMATH Keywords: reordering of series
zbMATH Keywords: theorem of Steinitz
author: Imre Bárány
author: V. S. Grinberg
reviewed by: P. Mani-Levitska
MaRDI profile type: Publication
cites work: A Vector-Sum Theorem and its Application to Improving Flow Shop Guarantees
full work available at URL: https://doi.org/10.1007/bf01857593
OpenAlex ID: W2094230726
Recommended article: Q5749882
Recommended article: Vector sum-intersection theorems
Recommended article: Q5430768
Recommended article: On the Vector Sum of Two Convex Sets in Space
Recommended article: Two-sided vector spaces
Recommended article: A Vector Form of Alexandrov's Theorem
Recommended article: Sum of dilates in vector spaces
Recommended article: Q3980665
Recommended article: A two-dimensional Birkhoff's theorem
description: scientific article; zbMATH DE number 3927800