Johnson, CRMarques, MD2018-12-072018-12-072005-071081-3810http://hdl.handle.net/10400.1/11482Identified 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.engjournal article10.13001/1081-3810.1176