Hao-Tian Jiang

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math.CO2026

An Exposition of the $O (lo g^{1/4} n)$ Bound for the Komlós Problem

Nikhil Bansal, Haotian Jiang

A conjecture of Komlós states that the combinatorial discrepancy of any matrix $A \in R^{m \times n}$ whose columns have Euclidean norm at most one is bounded by a universal c…

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 $n$ elements with degree $k$ has combinatorial discrepancy $O (k)$ . 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 $A \in {0, 1}^{m \times n}$ with degree at most $k$ (i.e., each column of $A$ has at most $…

An Exposition of the O(log1/4n) Bound for the Komlós Problem

Decoupling via Affine Spectral-Independence: Beck-Fiala and Komlós Bounds Beyond Banaszczyk

An Improved Bound for the Beck-Fiala Conjecture

An Exposition of the $O (lo g^{1/4} n)$ Bound for the Komlós Problem