A remark on Kashin's discrepancy argument and partial coloring in the Komlós conjecture

Abstract

In this expository note, we discuss an early partial coloring result of B. Kashin [C. R. Acad. Bulgare Sci., 1985]. Although this result only implies Spencer's six standard deviations [Trans. Amer. Math. Soc., 1985] up to a $\log \log n$ factor, Kashin's argument gives a simple proof of the existence of a constant discrepancy partial coloring in the setup of Komlós conjecture.

arXiv comment4 pages, an expository note