ELA, Volume 14, pp. 43-50, July 2005, abstract.

Patterns of Commutativity: The Commutant of the 
Full Pattern

Charles R. Johnson and Maria da Graca Marques

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.