Partial R-clones

In [Romov, ISMVL 2013] the first author introduced a type of partial clones as the intersection of some special infinite descending chains similar to I. Rosenberg
(1972) in the case of total clones. We provide a characterization of these clones in terms of their invariants, and propose a generalization of such clones, which we will call partial R-clones. We show that there are only finitely many partial R-clones. Furthermore, we investigate some properties related to their position in the lattice of partial clones.