Partitions and sums and products of integers
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- by Neil Hindman
- Trans. Amer. Math. Soc. 247 (1979), 227-245
- DOI: https://doi.org/10.1090/S0002-9947-1979-0517693-4
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Abstract:
The principal result of the paper is that, if $r < \omega$ and ${\{ {A_i}\} _{i < r}}$ is a partition of $\omega$, then there exist $i < r$ and infinite subsets B and C of $\omega$ such that $\sum F \in {A_i}$ and $\prod {G \in {A_i}}$ whenever F and G are finite nonempty subsets of B and C respectively. Conditions on the partition are obtained which are sufficient to guarantee that B and C can be chosen equal in the above statement, and some related finite questions are investigated.References
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Bibliographic Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 247 (1979), 227-245
- MSC: Primary 10A45; Secondary 05A17, 54A25
- DOI: https://doi.org/10.1090/S0002-9947-1979-0517693-4
- MathSciNet review: 517693