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

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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Correspondence to Diana Ojeda-Aristizabal.

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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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Mathematics Subject Classification (2000)

  • 05D10
  • 46B25