The existence of certain ultra-filters on 𝑁 and a conjecture of Graham and Rothschild

Hindman, Neil

doi:10.1090/S0002-9939-1972-0307926-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The existence of certain ultra-filters on $N$ and a conjecture of Graham and Rothschild
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by Neil Hindman PDF

Proc. Amer. Math. Soc. 36 (1972), 341-346 Request permission

Abstract:

The equivalence of a conjecture of Graham and Rothschild and the existence of certain ultrafilters on N is established. It is also shown that this conjecture is equivalent to an apparently stronger statement.

References

Problems and results on combinatorial number theory

R. L. Graham and B. L. Rothschild, Ramsey’s theorem for $n$-parameter sets, Trans. Amer. Math. Soc. 159 (1971), 257–292. MR 284352, DOI 10.1090/S0002-9947-1971-0284352-8