Discrepancy of Set-systems and Matrices

L. Lovász, J. Spencer, K. Vesztergombi

Research output: Contribution to journalArticle

72 Citations (Scopus)

Abstract

The discrepancy of a set-system is the minimum number d for which the vertices can be 2-coloured red and blue so that in each. of the given sets, the difference between the numbers of red and blue vertices is at most d. In this paper. we introduce various mathematically more tractable variants of this notion. We prove several inequalities relating these numbers, and formulate several further conjectures. We extend the notion to a general matrix, and formulate it as a problem of covering the unit cube by convex bodies.

Original languageEnglish
Pages (from-to)151-160
Number of pages10
JournalEuropean Journal of Combinatorics
Volume7
Issue number2
DOIs
Publication statusPublished - Jan 1 1986

Fingerprint

Set Systems
Discrepancy
Unit cube
Convex Body
Covering

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Discrepancy of Set-systems and Matrices. / Lovász, L.; Spencer, J.; Vesztergombi, K.

In: European Journal of Combinatorics, Vol. 7, No. 2, 01.01.1986, p. 151-160.

Research output: Contribution to journalArticle

Lovász, L. ; Spencer, J. ; Vesztergombi, K. / Discrepancy of Set-systems and Matrices. In: European Journal of Combinatorics. 1986 ; Vol. 7, No. 2. pp. 151-160.
@article{e2b2db8e2c9948aea6e64ce15e4110ee,
title = "Discrepancy of Set-systems and Matrices",
abstract = "The discrepancy of a set-system is the minimum number d for which the vertices can be 2-coloured red and blue so that in each. of the given sets, the difference between the numbers of red and blue vertices is at most d. In this paper. we introduce various mathematically more tractable variants of this notion. We prove several inequalities relating these numbers, and formulate several further conjectures. We extend the notion to a general matrix, and formulate it as a problem of covering the unit cube by convex bodies.",
author = "L. Lov{\'a}sz and J. Spencer and K. Vesztergombi",
year = "1986",
month = "1",
day = "1",
doi = "10.1016/S0195-6698(86)80041-5",
language = "English",
volume = "7",
pages = "151--160",
journal = "European Journal of Combinatorics",
issn = "0195-6698",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Discrepancy of Set-systems and Matrices

AU - Lovász, L.

AU - Spencer, J.

AU - Vesztergombi, K.

PY - 1986/1/1

Y1 - 1986/1/1

N2 - The discrepancy of a set-system is the minimum number d for which the vertices can be 2-coloured red and blue so that in each. of the given sets, the difference between the numbers of red and blue vertices is at most d. In this paper. we introduce various mathematically more tractable variants of this notion. We prove several inequalities relating these numbers, and formulate several further conjectures. We extend the notion to a general matrix, and formulate it as a problem of covering the unit cube by convex bodies.

AB - The discrepancy of a set-system is the minimum number d for which the vertices can be 2-coloured red and blue so that in each. of the given sets, the difference between the numbers of red and blue vertices is at most d. In this paper. we introduce various mathematically more tractable variants of this notion. We prove several inequalities relating these numbers, and formulate several further conjectures. We extend the notion to a general matrix, and formulate it as a problem of covering the unit cube by convex bodies.

UR - http://www.scopus.com/inward/record.url?scp=84966216165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966216165&partnerID=8YFLogxK

U2 - 10.1016/S0195-6698(86)80041-5

DO - 10.1016/S0195-6698(86)80041-5

M3 - Article

AN - SCOPUS:84966216165

VL - 7

SP - 151

EP - 160

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

IS - 2

ER -