Ramsey’s theorem for spaces
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- by Joel H. Spencer PDF
- Trans. Amer. Math. Soc. 249 (1979), 363-371 Request permission
Abstract:
A short proof is given of the following known result. For all k, r, t there exists n so that if the t-spaces of an n-space are r-colored there exists a k-space all of whose t-spaces are the same color. Here t-space refers initially to a t-dimensional affine space over a fixed finite field. The result is also shown for a more general notion of t-space.References
- R. L. Graham, K. Leeb, and B. L. Rothschild, Ramsey’s theorem for a class of categories, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 119–120. MR 306009, DOI 10.1073/pnas.69.1.119
- 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
- A. W. Hales and R. I. Jewett, Regularity and positional games, Trans. Amer. Math. Soc. 106 (1963), 222–229. MR 143712, DOI 10.1090/S0002-9947-1963-0143712-1
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 249 (1979), 363-371
- MSC: Primary 05A99; Secondary 05C55
- DOI: https://doi.org/10.1090/S0002-9947-1979-0525678-7
- MathSciNet review: 525678