Partitions and sums and products of integers
Author:
Neil Hindman
Journal:
Trans. Amer. Math. Soc. 247 (1979), 227245
MSC:
Primary 10A45; Secondary 05A17, 54A25
MathSciNet review:
517693
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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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Hindman, Finite sums from sequences within cells of a partition of
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, Partitions and sums of integers with repetition, J. Combinatorial Theory Ser. A (to appear).
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 [1]
 J. Baumgartner, A short proof of Hindman's theorem, J. Combinatorial Theory Ser. A 17 (1974), 384386. MR 0354394 (50:6873)
 [2]
 W. Comfort, Some recent applications of ultrafilters to topology, (Proc. Fourth 1976 Prague Topological Symposium), Lecture Notes in Math., SpringerVerlag, Berlin and New York, 1978. MR 0451187 (56:9474)
 [3]
 , Ultrafilters: Some old and some new results, Bull. Amer. Math. Soc. 83 (1977), 417455. MR 0454893 (56:13136)
 [4]
 L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
 [5]
 S. Glazer, Ultrafilters and semigroup combinatorics, J. Combinatorial Theory Ser. A (to appear).
 [6]
 N. Hindman, Finite sums from sequences within cells of a partition of N, J. Combinatorial Theory Ser. A 17 (1974), 111. MR 0349574 (50:2067)
 [7]
 , Partitions and sums of integers with repetition, J. Combinatorial Theory Ser. A (to appear).
 [8]
 , The existence of certain ultrafilters on N and a conjecture of Graham and Rothschild, Proc. Amer. Math. Soc. 36 (1972), 341346. MR 0307926 (46:7041)
 [9]
 A. Tarski, Sur la décomposition des ensembles en sousensembles presque disjoints, Fund. Math. 12 (1928), 188205.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905176934
PII:
S 00029947(1979)05176934
Keywords:
Partitions,
ultrafilters,
sums,
products
Article copyright:
© Copyright 1979
American Mathematical Society
