Multi-dimensional Ramsey theorems — An example

Abstract

In [1] V. Bergelson and N. Hindman used a 6-cell partition of [N]2 to show that one cannot combine their major result with the Milliken-Taylor theorem and asked if one can provide an example with fewer than 6-cells. In this note we show that their 6-cell example can be collapsed into a 5-cell example.

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References

  1. [1]

    V. Bergelson andN. Hindman: Ultrafilters and multidimensional Ramsey Theorems,Combinatorica 9 (1989), 1–7.

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  2. [2]

    N. Hindman: Partitions and Sums and products—two counter examples,J. Comb. Theory (Series A)29 (1980), 113–120.

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The author gratefully acknowledges support from the Council on Research of Louisiana State University.

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Lisan, A.T. Multi-dimensional Ramsey theorems — An example. Combinatorica 12, 363–365 (1992). https://doi.org/10.1007/BF01285824

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AMS subject classification code (1991)

  • 05 D 10
  • 05 A 18