Geometric & Functional Analysis GAFA

, Volume 7, Issue 2, pp 322–337

Lower bounds of tower type for Szemerédi's uniformity lemma

  • W.T. Gowers

DOI: 10.1007/PL00001621

Cite this article as:
Gowers, W. GAFA, Geom. funct. anal. (1997) 7: 322. doi:10.1007/PL00001621

Abstract.

It is known that the size of the partition obtained in Szemerédi's Uniformity Lemma can be bounded above by a number given by a tower of 2s of height proportional to \(\epsilon^{-5}\), where \(\epsilon\) is the desired accuracy. In this paper, we first show that the bound is necessarily of tower type, obtaining a lower bound given by a tower of 2s of height proportional to \( \log{(1/ \epsilon)} \)). We then give a different construction which improves the bound, even for certain weaker versions of the statement.

Copyright information

© Birkhäuser Verlag, Basel, 1997

Authors and Affiliations

  • W.T. Gowers
    • 1
  1. 1.W.T. Gowers, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, England, e-mail: W.T.Gowers@pmms.cam.ac.ukGB