A Fourier-Analytic Approach for the Discrepancy of Random Set Systems

  title={A Fourier-Analytic Approach for the Discrepancy of Random Set Systems},
  author={Rebecca Hoberg and Thomas Rothvoss},
One of the prominent open problems in combinatorics is the discrepancy of set systems where each element lies in at most $t$ sets. The Beck-Fiala conjecture suggests that the right bound is $O(\sqrt{t})$, but for three decades the only known bound not depending on the size of the set system has been $O(t)$. Arguably we currently lack techniques for breaking that barrier. In this paper we introduce discrepancy bounds based on Fourier analysis. We demonstrate our method on random set systems… 
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