Problem
Research questions and friction points this paper is trying to address.
Komlós conjecture
vectors
signs
infinity norm
An elementary proof of the Komlós conjecture
🤖 AI Summary
本文通过简化Guo, Fang和Lu的证明方法，使用初等组合、概率论及基础微积分工具，证明了Komlós猜想。
📝 Abstract
We give an elementary proof of the Komlós 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
elementary proof
Komlós conjecture
simplification
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