  We prove that all the correlation functions in the $(1,q)$ models are
calculable using only the Virasoro and the $W^{(3)}$ constraints. This result
is based on the invariance of correlators with respect to an interchange of the
order of the operators they contain.
  In terms of the topological recursion relations, it means that only two and
three contacts and the corresponding degenerations of the underlying surfaces
are relevant. An algorithm to compute correlators for any $q$ and at any genus
is presented and demonstrated through some examples. On route to these results,
some interesting polynomial identities, which are generalizations of Abel's
identity, were discovered. }
