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Extensions of the Polynomial Hales–Jewett Theorem

Published online by Cambridge University Press:  01 September 2007

MARK WALTERS
MARK WALTERS*
Affiliation:
Peterhouse, Cambridge, CB2 1RD, UK (e-mail: [email protected])
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Abstract

In this paper we prove polynomial versions of the Carlson–Simpson theorem and the Graham–Rothschild theorem on parameter sets. To do so we prove a useful extension of the polynomial Hales–Jewett theorem.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 5 , September 2007 , pp. 789 - 803
Copyright
Copyright © Cambridge University Press 2006

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References

[1]Bergelson, V. and Leibman, A. (1996) Polynomial extensions of Van der Waerden and Szemerédi theorems. J. Amer. Math. Soc. 9 725–753.Google Scholar
[2]Bergelson, V. and Leibman, A. (1999) Set polynomials and polynomial extension of the Hales–Jewett theorem. Ann. of Math. 150 33–75.Google Scholar
[3]Carlson, T. J. and Simpson, S. G. (1984) A dual form of Ramsey's theorem. Adv. Math. 53 265–290.Google Scholar
[4]Comfort, W. (1977) Ultrafilters: Some old and some new results. Bull. Amer. Math. Soc. 83 417–455.Google Scholar
[5]Graham, R. L. and Rothschild, B. (1971) Ramsey's theorem for n parameter sets. Trans. Amer. Math. Soc. 159 257–292.Google Scholar
[6]Hales, A. W. and Jewett, R. I. (1963) Regularity and positional games. Trans. Amer. Math. Soc. 106 222–229.Google Scholar
[7]McCutcheon, R. (2000) Elemental Methods in Ergodic Ramsey Theory, Vol. 1722 of Lecture Notes in Computer Science, Springer.Google Scholar
[8]McCutcheon, R. (2000) Two new extensions of the Hales–Jewett theorem. Electron. J. Combin. 7 R49.Google Scholar
[9]McCutcheon, R. (2001) An infinitary polynomial Hales–Jewett theorem. Israel J. Math. 121 157–172.CrossRefGoogle Scholar
[10]Shelah, S. (2002) A partition theorem. Sci. Math. Jpn. 56 413–438.Google Scholar
[11]Walters, M. (2000) Combinatorial proofs of the polynomial Van der Waerden theorem and polynomial Hales–Jewett theorem. J. London Math. Soc. 61 1–12.Google Scholar
[12]Walters, M. (2000) Ramsey theory, discrepancy theory and related areas. PhD thesis.Google Scholar