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math.CO2025
Decoupling via Affine Spectral-Independence: Beck-Fiala and Komlós Bounds Beyond Banaszczyk
Nikhil Bansal, Haotian Jiang
The Beck-Fiala Conjecture [Discrete Appl. Math, 1981] asserts that any set system of elements with degree has combinatorial discrepancy . A substantial general…
math.CO2025
An Improved Bound for the Beck-Fiala Conjecture
Nikhil Bansal, Haotian Jiang
In 1981, Beck and Fiala [Discrete Appl. Math, 1981] conjectured that given a set system with degree at most (i.e., each column of has at most $…