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- W2001432931 abstract "For each positive integer n , let the set of all 2-colorings of the interval [1, n ]={1, 2, …,, n } be given the uniform probability distribution, that is, each of the 2 n colorings is assigned probability 2 − n . Let f be any function such that f ( k )/log k →∞ as k →∞. For convenience we assume that f ( k ) 2 k is always a positive integer. We show that the probability that a random 2-coloring of [1, f ( k ) 2 k ] produces a monochromatic k -term arithmetic progression tends to 1 as k →∞. We call f ( k ) 2 k a pseudo upper bound for the van der Waerden function. We also prove the “density version” of this result." @default.
- W2001432931 created "2016-06-24" @default.
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- W2001432931 date "1999-07-01" @default.
- W2001432931 modified "2023-09-28" @default.
- W2001432931 title "A Pseudo Upper Bound for the van der Waerden Function" @default.
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- W2001432931 doi "https://doi.org/10.1006/jcta.1998.2936" @default.
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