ERDOS SEMI-GROUPS, ARITHMETIC PROGRESSIONS, AND SZEMEREDI'S THEOREM

被引：0

作者：

Yu, Han ^{[1
]}

机构：

[1] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland

来源：

REAL ANALYSIS EXCHANGE | 2019年 / 44卷 / 01期

关键词：

Hausdorff dimension; sum sets; Szemeredi theorem; PROOF;

D O I：

10.14321/realanalexch.41.1.0101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce and study a certain type of sub semi-group of R/Z which turns out to be closely related to Szemeredi's theorem on arithmetic progressions.

引用

页码：101 / 118

页数：18

共 15 条

[1]

Bishop C.J., 2016, Cambridge Studies in Advanced Mathematics

[2]

ERDOS P, 1966, J REINE ANGEW MATH, V221, P203

[3]

Falconer K., 2015, FRACTAL GEOMETRY STO, VV

[4]

Falconer K., 2004, FRACTAL GEOMETRY MAT

[5]

Fraser J., 2018, DIMENSION GROWTH ITE

[6] Dimensions of Sets Which Uniformly Avoid Arithmetic Progressions [J].

Fraser, Jonathan M. ;

Saito, Kota ;

Yu, Han .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019, 2019 (14) :4419-4430

[7] Arithmetic patches, weak tangents, and dimension [J].

Fraser, Jonathan M. ;

Yu, Han .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2018, 50 (01) :85-95

[8] THE ERGODIC THEORETICAL PROOF OF SZEMEREDIS THEOREM [J].

FURSTENBERG, H ;

KATZNELSON, Y ;

ORNSTEIN, D .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 7 (03) :527-552

[9] A new proof of Szemeredi's theorem [J].

Gowers, WT .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2001, 11 (03) :465-588

[10] PROBABILITY-INEQUALITIES FOR SUMS OF BOUNDED RANDOM-VARIABLES [J].

HOEFFDING, W .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1963, 58 (301) :13-+

← 1 2 →