Monochromatic combinatorial lines of length three

Conlon, David

doi:10.1090/proc/15739

Monochromatic combinatorial lines of length three
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Proc. Amer. Math. Soc. 150 (2022), 1-4 Request permission

Abstract:

We show that there is a positive constant $c$ such that any colouring of the cube $[3]^n$ in $c \log \log n$ colours contains a monochromatic combinatorial line.

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