Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Ramsey’s theorem for $n$-parameter sets

Authors: R. L. Graham and B. L. Rothschild
Journal: Trans. Amer. Math. Soc. 159 (1971), 257-292
MSC: Primary 05.04
MathSciNet review: 0284352
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Classes of objects called $n$-parameter sets are defined. A Ramsey theorem is proved to the effect that any partitioning into $r$ classes of the $k$-parameter subsets of any sufficiently large $n$-parameter set must result in some $l$-parameter subset with all its $k$-parameter subsets in one class. Among the immediate corollaries are the lower dimensional cases of a Ramsey theorem for finite vector spaces (a conjecture of Rota), the theorem of van der Waerden on arithmetic progressions, a set theoretic generalization of a theorem of Schur, and Ramsey’s Theorem itself.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 05.04

Retrieve articles in all journals with MSC: 05.04

Additional Information

Keywords: Ramsey’s Theorem, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">-parameter set, finite vector space
Article copyright: © Copyright 1971 American Mathematical Society