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Paper:

TR26-188 | 17th September 2026 20:00

An elementary proof of the Komlos conjecture

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TR26-188
Authors: Sankeerth Rao Karingula, Shachar Lovett
Publication: 17th September 2026 20:01
Downloads: 345
Keywords: 


Abstract:

We give an elementary proof of the Komlos conjecture by simplifying the recent proof of Guo, Fang, and Lu. We show that any vectors $v_1,\ldots,v_n\in\mathbb{R}^d$ with $\|v_i\|_2\le1$ admit signs $\varepsilon_i\in\{-1,1\}$ such that $\|\sum_{i=1}^n\varepsilon_i v_i\|_\infty\le36$. The proof uses only elementary combinatorial and probabilistic arguments and basic calculus.



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