New York Journal of Mathematics
Volume 11 (2005) 519-538


Neil Hindman and Dona Strauss

Image partition regularity over the integers, rationals and reals

Published: November 1, 2005
Keywords: Image partition regularity, Rado's Theorem, Subsemigroups of R
Subject: 05D10

There is only one reasonable definition of kernel partition regularity over any subsemigroup of the reals. On the other hand, there are several reasonable definitions of image partition regularity. We establish the exact relationships that can hold among these various notions for finite matrices and infinite matrices with rational entries. We also introduce some hybrid notions and describe their relationship to what is probably the major unsolved problem in kernel partition regularity, namely whether an infinite matrix which is kernel partition regular over Q must be kernel partition regular over N.


The first author acknowledges support received from the National Science Foundation (USA) via grant DMS 0243586.

Author information

Neil Hindman:
Department of Mathematics, Howard University, Washington, DC 20059, USA

Dona Strauss:
Department of Pure Mathematics, University of Hull, Hull HU6 7RX, UK