The submaximal clones on the three-element set with finitely many relative R-classes

Discussiones Mathematicae - General Algebra and Applications, 30(1) (2010), 7-33
http://dx.doi.org/10.7151/dmgaa.1160

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.