Ramsey’s theorem for $n$-parameter sets
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- by R. L. Graham and B. L. Rothschild PDF
- Trans. Amer. Math. Soc. 159 (1971), 257-292 Request permission
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
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 159 (1971), 257-292
- MSC: Primary 05.04
- DOI: https://doi.org/10.1090/S0002-9947-1971-0284352-8
- MathSciNet review: 0284352