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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Partitions and sums and products of integers
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by Neil Hindman PDF
Trans. Amer. Math. Soc. 247 (1979), 227-245 Request permission

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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Additional 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