  We contribute to the theory for minimal liftings of cut-generating functions.
In particular, we give three operations that preserve the so-called covering
property of certain structured cut-generating functions. This has the
consequence of vastly expanding the set of undominated cut generating functions
which can be used computationally, compared to known examples from the
literature. The results of this paper are significant generalizations of
previous results from the literature on such operations, and also use
completely different proof techniques which we feel are more suitable for
attacking future research questions in this area.
