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 | References | Similar Articles | Additional Information

Abstract: The principal result of the paper is that, if and is a partition of , then there exist and infinite subsets *B* and *C* of such that and 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0517693-4

Keywords:
Partitions,
ultrafilters,
sums,
products

Article copyright:
© Copyright 1979
American Mathematical Society