Image partition regular matrices and concepts of largeness, II - Hindman, Neil; Strauss, Dona (Topology Proceedings, 2026)
Abstract. Let u and v be positive integers and let A be a u × v matrix with rational entries. We determine several characterizations of the property that whenever B is a piecewise syndetic subset of the set N of positive integers, {x N^v: A x B^u} is piecewise syndetic in N^v as well as the corresponding property with Z replacing N. We investigate related phenomena for several other notions of largeness in a semigroup.