 

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 


Abstract
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.


Acknowledgements
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
nhindman@howard.edu
http://members.aol.com/nhindman/
Dona Strauss:
Department of Pure Mathematics, University of Hull, Hull HU6 7RX, UK
d.strauss@hull.ac.uk

