Balancing unit vectors

Research output: Contribution to journalArticle

Abstract

Given any family u1,..., um of vectors in Euclidean n-space of Euclidean norm at most unity it is shown that at least one of the sums ±u1 ± ... um has norm at most n 1 2. Probabilistic techniques are used.

Original languageEnglish (US)
Pages (from-to)349-350
Number of pages2
JournalJournal of Combinatorial Theory, Series A
Volume30
Issue number3
StatePublished - May 1981

Fingerprint

Euclidean norm
Unit vector
Balancing
Euclidean
Norm
Family

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Balancing unit vectors. / Spencer, Joel.

In: Journal of Combinatorial Theory, Series A, Vol. 30, No. 3, 05.1981, p. 349-350.

Research output: Contribution to journalArticle

@article{2a0daed59808457b93bb03a283f5db95,
title = "Balancing unit vectors",
abstract = "Given any family u1,..., um of vectors in Euclidean n-space of Euclidean norm at most unity it is shown that at least one of the sums ±u1 ± ... um has norm at most n 1 2. Probabilistic techniques are used.",
author = "Joel Spencer",
year = "1981",
month = "5",
language = "English (US)",
volume = "30",
pages = "349--350",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - Balancing unit vectors

AU - Spencer, Joel

PY - 1981/5

Y1 - 1981/5

N2 - Given any family u1,..., um of vectors in Euclidean n-space of Euclidean norm at most unity it is shown that at least one of the sums ±u1 ± ... um has norm at most n 1 2. Probabilistic techniques are used.

AB - Given any family u1,..., um of vectors in Euclidean n-space of Euclidean norm at most unity it is shown that at least one of the sums ±u1 ± ... um has norm at most n 1 2. Probabilistic techniques are used.

UR - http://www.scopus.com/inward/record.url?scp=49149137147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49149137147&partnerID=8YFLogxK

M3 - Article

VL - 30

SP - 349

EP - 350

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 3

ER -