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Finite forms of Gowers’ theorem on the oscillation stability of C 0

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Abstract

We give a constructive proof of the finite version of Gowers’ FIN k Theorem for both the positive and the general case and analyse the corresponding upper bounds provided by the proofs.

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References

  1. J. E. Baumgartner: A short proof of Hindman’s theorem, J. Combinatorial Theory Ser. A 17 (1974), 384–386.

    Article  MathSciNet  MATH  Google Scholar 

  2. W. T. Gowers: Lipschitz functions on classical spaces, European J. Combin. 13 (1992), 141–151.

    Article  MathSciNet  MATH  Google Scholar 

  3. W. T. Gowers: A new proof of Szemerédi’s theorem, Geom. Funct. Anal. 11 (2001), 465–588.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. L. Graham, B. L. Rothschild and J.H. Spencer: Ramsey theory, John Wiley & Sons Inc., New York (1980), Wiley-Interscience Series in Discrete Mathematics, A Wiley-Interscience Publication.

    MATH  Google Scholar 

  5. N. Hindman: Finite sums from sequences within cells of a partition of N, J. Combinatorial Theory Ser. A 17 (1974), 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Kanellopoulos: A proof of W. T. Gowers’ c0 theorem, Proc. Amer. Math. Soc. 132 (2004), 3231–3242 (electronic).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. D. Milman and G. Schechtman: Asymptotic theory of finite-dimensional normed spaces, volume 1200 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (1986). With an appendix by M. Gromov.

    Google Scholar 

  8. E. Odell, H. P. Rosenthal and Th. Schlumprecht: On weakly null FDDs in Banach spaces, Israel J. Math. 84 (1993), 333–351.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. D. Taylor: Bounds for the disjoint unions theorem, J. Combin. Theory Ser. A 30 (1981), 339–344.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Todorcevic: Introduction to Ramsey spaces, volume 174 of Annals of Mathematics Studies, Princeton University Press, Princeton, NJ (2010).

    Google Scholar 

  11. K. Tyros: Primitive recursive bounds for the finite version of Gowers’ c0 theorem. Available at arxiv.org/abs/1401.8073.

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Authors and Affiliations

  1. Mathematics Department, University of Toronto, Toronto, ON, Canada, M5S 2E4

    Diana Ojeda-Aristizabal

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  1. Diana Ojeda-Aristizabal
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Correspondence to Diana Ojeda-Aristizabal.

Additional information

The research of the author presented in this paper was partially supported by NSF grants DMS-0757507 and DMS-1262019. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the author and do not necessarily re ect the views of the National Science Foundation.

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Ojeda-Aristizabal, D. Finite forms of Gowers’ theorem on the oscillation stability of C 0 . Combinatorica 37, 143–155 (2017). https://doi.org/10.1007/s00493-015-3223-7

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  • DOI: https://doi.org/10.1007/s00493-015-3223-7

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