  We introduce a $q,t$-enumeration of Dyck paths which are forced to touch the
main diagonal at specific points and forbidden to touch elsewhere and
conjecture that it describes the action of the Macdonald theory $\nabla$
operator applied to a Hall-Littlewood polynomial. Our conjecture refines
several earlier conjectures concerning the space of diagonal harmonics
including the "shuffle conjecture" (Duke J. Math. $\mathbf {126}$ (2005), pp.
195-232) for $\nabla e_n[X]$. We bring to light that certain generalized
Hall-Littlewood polynomials indexed by compositions are the building blocks for
the algebraic combinatorial theory of $q,t$-Catalan sequences and we prove a
number of identities involving these functions.
