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An Improvement of the Beck–Fiala Theorem

Part of: Extremal combinatorics Graph theory Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  06 July 2015

BORIS BUKH
BORIS BUKH*
Affiliation:
Department of Mathematical Sciences, Wean Hall 6113, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: [email protected])
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Abstract

In 1981 Beck and Fiala proved an upper bound for the discrepancy of a set system of degree d that is independent of the size of the ground set. In the intervening years the bound has been decreased from 2d − 2 to 2d − 4. We improve the bound to 2d − log*d.

MSC classification

Primary: 05D05: Extremal set theory
Secondary: 11K38: Irregularities of distribution, discrepancy 05C15: Coloring of graphs and hypergraphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 3 , May 2016 , pp. 380 - 398
Copyright
Copyright © Cambridge University Press 2015 

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References

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