# 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 language English 151-160 10 European Journal of Combinatorics 7 2 https://doi.org/10.1016/S0195-6698(86)80041-5 Published - Jan 1 1986

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.
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