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Ben Green presents super-polynomial lower bounds for off-diagonal van der Waerden numbers W(3,k): arxiv.org/abs/2102.01543, via gilkalai.wordpress.com/2021/02

W(3,k) is the smallest N such that a 2-coloring of [N] has a 3-term arithmetic progression of one color or a k-term progression of the other. It was previously known to be subexponential and thought to be only quadratic.

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