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Multi-dimensional Ramsey theorems — An example

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

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

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, 70803, Baton Rouge, Louisiana, U.S.A.

    Amha Tume Lisan

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  1. Amha Tume Lisan
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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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  • DOI: https://doi.org/10.1007/BF01285824

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