Hindman, Neil Partitions and pairwise sums and products. (English) Zbl 0542.05011 J. Comb. Theory, Ser. A 37, 46-60 (1984). A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey theory question is shown to have different answers for two and three cell partitions. Cited in 3 Documents MSC: 05A17 Combinatorial aspects of partitions of integers 05C55 Generalized Ramsey theory Keywords:seven cell partition; sums; products PDF BibTeX XML Cite \textit{N. Hindman}, J. Comb. Theory, Ser. A 37, 46--60 (1984; Zbl 0542.05011) Full Text: DOI References: [1] Gillman, L.; Jerison, M., Rings of Continuous Functions (1960), Van Nostrand: Van Nostrand Princeton, NJ · Zbl 0093.30001 [2] Graham, R., Rudiments of Ramsey Theory (1981), Amer. Math. Soc: Amer. Math. Soc Providence, RI [3] Graham, R.; Rothschild, B.; Spencer, J., Ramsey Theory (1980), Wiley: Wiley New York [4] Hindman, N., Partitions and sums and products—Two counterexamples, J. Combin. Theory Ser. A, 29, 113-120 (1980) · Zbl 0443.05010 [5] Hindman, N., Partitions and sums of integers with repetition, J. Combin. Theory Ser. A, 27, 19-32 (1979) · Zbl 0419.05001 [6] Hindman, N., Simultaneous idempotents in \(βNN\) and finite sums and products in \(N\), (Proc. Amer. Math. Soc., 77 (1979)), 150-154 · Zbl 0417.05005 [7] Hindman, N., Ultrafilters and combinatorial number theory, (Lecture Notes in Math. No. 751 (1979), Springer-Verlag: Springer-Verlag Berlin), 119-184 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.