Open problems in partition regularity

被引：38

作者：

Hindman, N ^{[1
]}

Leader, I

Strauss, D

机构：

[1] Howard Univ, Dept Math, Washington, DC 20059 USA

[2] Ctr Math Sci, Dept Pure Math & Math Stat, Cambridge, England

[3] Univ Hull, Dept Pure Math, Kingston Upon Hull HU6 7RX, N Humberside, England

来源：

COMBINATORICS PROBABILITY & COMPUTING | 2003年 / 12卷 / 5-6期

关键词：

D O I：

10.1017/S0963548303005716

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A finite or infinite matrix A with rational entries is called partition regular if, whenever the natural numbers are finitely coloured, there is a monochromatic vector x with Ax = 0. Many of the classical theorems of Ramsey Theory may naturally be interpreted as assertions that particular matrices are partition regular. While in the finite case partition regularity is well understood, very little is known in the infinite case. Our aim in this paper is to present some of the natural and appealing open problems in the area.

引用

页码：571 / 583

页数：13

共 32 条

[1]

[Anonymous], 1973, FUND MATH

[2] All-sums sets in (0, 1] - Category and measure [J].