Duality for image and kernel partition regularity of infinite matrices
Combinatorics
2016-09-13 v1
Abstract
A matrix A is image partition regular over Q provided that whenever Q - {0} is finitely coloured, there is a vector x with entries in Q - {0} such that the entries of Ax are monochromatic. It is kernel partition regular over Q provided that whenever Q - {0} is finitely coloured, the matrix has a monochromatic member of its kernel. We establish a duality for these notions valid for both finite and infinite matrices. We also investigate the extent to which this duality holds for matrices partition regular over proper subsemigroups of Q.
Cite
@article{arxiv.1609.03225,
title = {Duality for image and kernel partition regularity of infinite matrices},
author = {Neil Hindman and Imre Leader and Dona Strauss},
journal= {arXiv preprint arXiv:1609.03225},
year = {2016}
}