  We conjecture a relation between generalized quiver partition functions and
generating functions for symmetrically colored HOMFLY-PT polynomials and
corresponding HOMFLY-PT homology Poincar\'e polynomials of a knot $K$. We
interpret the generalized quiver nodes as certain basic holomorphic curves with
boundary on the knot conormal $L_K$ in the resolved conifold, and the adjacency
matrix as measuring their boundary linking. The simplest such curves are
embedded disks with boundary in the primitive homology class of $L_K$, other
basic holomorphic curves consists of two parts: an embedded punctured sphere
and a multiply covered punctured disk with boundary in a multiple of the
primitive homology class of $L_K$. We also study recursion relations for the
partition functions connected to knot homologies. We show that, after a
suitable change of variables, any (generalized) quiver partition function
satisfies the recursion relation of a single toric brane in $\mathbb{C}^3$.
