Lower bounds of tower type for Szemeredi's Uniformity Lemma

被引：115

作者：

Gowers, WT

机构：

[1] Dept. of Pure Math. and Math. Stat., Cambridge CB2 1SB

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 1997年 / 7卷 / 02期

关键词：

Lower Bound; Weak Version; Tower Type; Uniformity Lemma;

D O I：

10.1007/PL00001621

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that the size of the partition obtained in Szemeredi'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.

引用

页码：322 / 337

页数：16