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.
References
V. Bergelson andN. Hindman: Ultrafilters and multidimensional Ramsey Theorems,Combinatorica 9 (1989), 1–7.
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
Additional information
The author gratefully acknowledges support from the Council on Research of Louisiana State University.