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Generalized van der Waerden numbers

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Abstract

Certain generalizations of arithmetic progressions are used to define numbers analogous to the van der Waerden numbers. Several exact values of the new numbers are given, and upper bounds for these numbers are obtained. In addition, a comparison is made between the number of different arithmetic progressions and the number of different generalized arithmetic progressions.

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References

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Authors and Affiliations

  1. Department of Mathematics, Hofstra University, 11550, Hempstead, NY, USA

    Bruce M. Landman

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  1. Bruce M. Landman
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Landman, B.M. Generalized van der Waerden numbers. Graphs and Combinatorics 2, 351–356 (1986). https://doi.org/10.1007/BF01788109

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  • DOI: https://doi.org/10.1007/BF01788109

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