A canonical restricted version of van der waerden’s theorem


It is shown that there is a subsetS of integers containing no (k+1)-term arithmetic progression such that if the elements ofS are arbitrarily colored (any number of colors),S will contain ak-term arithmetic progression for which all of its terms have the same color, or all have distinct colors.

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Prömel, H.J., Rothschild, B.L. A canonical restricted version of van der waerden’s theorem. Combinatorica 7, 115–119 (1987). https://doi.org/10.1007/BF02579207

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AMS subject classification (1980)

  • 05 C 55