  We derive two multivariate generating functions for three-dimensional Young
diagrams (also called plane partitions). The variables correspond to a
colouring of the boxes according to a finite Abelian subgroup G of SO(3). We
use the vertex operator methods of Okounkov--Reshetikhin--Vafa for the easy
case G = Z/n; to handle the considerably more difficult case G=Z/2 x Z/2, we
will also use a refinement of the author's recent q--enumeration of pyramid
partitions.
  In the appendix, we relate the diagram generating functions to the
Donaldson-Thomas partition functions of the orbifold C^3/G. We find a
relationship between the Donaldson-Thomas partition functions of the orbifold
and its G-Hilbert scheme resolution. We formulate a crepant resolution
conjecture for the Donaldson-Thomas theory of local orbifolds satisfying the
Hard Lefschetz condition.
