Partition regularity in the rationals

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Barber, Ben¹  Hindman, Neil²  Leader, Imre¹ 

[1] Ctr Math Sci, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England

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

关键词: Partition regularity;    Ramsey theory;    Finite Sums theorem;   

DOI  :  10.1016/j.jcta.2013.05.011

来源: Elsevier

【 摘 要 】

A system of homogeneous linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, the system has a monochromatic solution. The Finite Sums theorem provided the first example of an infinite partition regular system of equations. Since then, other such systems of equations have been found, but each can be viewed as a modification of the Finite Sums theorem. We present here a new infinite partition regular system of equations that appears to arise in a genuinely different way. This is the first example of a partition regular system in which a variable occurs with unbounded coefficients. A modification of the system provides an example of a system that is partition regular over Q but not N, settling another open problem. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free