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Small subset sums

Ambrus, G; Barany, I; Grinberg, V; (2016) Small subset sums. Linear Algebra and its Applications , 499 pp. 66-78. 10.1016/j.laa.2016.02.035. Green open access

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Abstract

Let ‖.‖ be a norm in Rd whose unit ball is B . Assume that V⊂B is a finite set of cardinality n , with ∑v∈Vv=0. We show that for every integer k with 0≤k≤n, there exists a subset U of V consisting of k elements such that ‖∑v∈Uv‖≤⌈d/2⌉. We also prove that this bound is sharp in general. We improve the estimate to View the MathML source for the Euclidean and the max norms. An application on vector sums in the plane is also given.

Type: Article
Title: Small subset sums
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.laa.2016.02.035
Publisher version: http://doi.org/10.1016/j.laa.2016.02.035
Language: English
Additional information: Copyright © 2016 Elsevier Ltd. All rights reserved. This is an Open Access article made available under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licenses are available at http://creativecommons.org/ licenses/by/4.0. Access may be initially restricted by the publisher.
Keywords: Vector sums; Steinitz theorem; Normed spaces
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1503479
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