An improvement of the Beck-Fiala theorem

Published 25 Jun 2013 in math.CO | (1306.6081v3)

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.

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Boris Bukh

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