Patterns of commutativity: the commutant of the full pattern,

Abstract

Identified are a number of conditions on square patterns that are closely related to
allowing commutativity with the full pattern. Implications and examples that show non-implications
are given, along with a graph that summarizes the provided information. A complete description of
commutativity with the full pattern is given in both the irreducible case and the reducible case in
which there are two irreducible components.