  We give combinatorial proofs that certain families of differences of products
of Schur functions are monomial-positive. We show in addition that such
monomial-positivity is to be expected of a large class of generating functions
with combinatorial definitions similar to Schur functions. These generating
functions are defined on posets with labelled Hasse diagrams and include for
example generating functions of Stanley's $(P,\omega)$-partitions.
