A canonical restricted version of van der waerden’s theorem

Combinatorica volume 7, pages115–119(1987)Cite this article

Abstract

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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Affiliations

  1. University of California, 90024, Los Angeles, USA

    H. -J. Prömel

  2. Inst. für Operations Research, Universität Bonn, 5300, Bonn-I, West Germany

    H. -J. Prömel & B. L. Rothschild

Authors
  1. H. -J. Prömel
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  2. B. L. Rothschild
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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