New York Journal of Mathematics
Volume 26 (2020), 230-260


Neil Hindman and Dona Strauss

Image partition regular matrices and concepts of largeness

view    print

Published: February 20, 2020.
Keywords: Image partition regularity, preservation of size, Ramsey Theory.
Subject: 05D10, 22A15.

We show that for several notions of largeness in a semigroup, if u,v ∈ N, A is a u x v matrix satisfying restrictions that vary with the notion of largeness, and if C is a large subset of N, then {x ∈ Nv:Ax ∈ Cu} is large in Nv. We show that in most cases the restrictions on A are necessary. Several other results, including some generalizations, are also obtained. Included is a simple proof that if u > 1, then β(Nv) is not isomorphic to (βN)u.



Author information

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


Dona Strauss:
Department of Pure Mathematics
University of Leeds
Leeds LS2 9J2, UK