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- W2964146593 abstract "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 rightbound is [MATH HERE], but for three decades the only known bound not depending on the size of 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. Suppose one has n elements and m sets containing each element independently with probability p. We prove that in the regime of n ≥ Θ (m2log(m)), the discrepancy is at most 1 with high probability. Previously a result of Ezra and Lovett gave a bound of O(1) under the stricter assumption that n » mt." @default.
- W2964146593 created "2019-07-30" @default.
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- W2964146593 date "2019-01-06" @default.
- W2964146593 modified "2023-09-24" @default.
- W2964146593 title "A fourier-analytic approach for the discrepancy of random set systems" @default.
- W2964146593 doi "https://doi.org/10.5555/3310435.3310591" @default.
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