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Open Problems in Partition Regularity

Published online by Cambridge University Press:  03 December 2003

Neil Hindman ,
Imre Leader  and
Dona Strauss
Neil Hindman*
Affiliation:
Department of Mathematics, Howard University, Washington, DC 20059, USA
Imre Leader*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK
Dona Strauss*
Affiliation:
Department of Pure Mathematics, University of Hull, Hull HU6 7RX, UK
*
(e-mail: nhindman@aol.comhttp://members.aol.com/nhindman/)
(e-mail: i.leader@dpmms.cam.ac.uk)
(e-mail: d.strauss@hull.ac.uk)
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Abstract

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 . 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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 5-6: This issue contains volume twelve, parts five and six , November 2003 , pp. 571 - 583
Copyright
Copyright © Cambridge University Press 2003

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Footnotes

†

Support received from the National Science Foundation (USA) via grant DMS-0070593.