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Transactions of the American Mathematical Society

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

 

 

Partitions and sums and products of integers


Author: Neil Hindman
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0517693-4
Keywords: Partitions, ultrafilters, sums, products
Article copyright: © Copyright 1979 American Mathematical Society