We derive two multivariate generating functions for three-dimensional (3D) Young diagrams (also called plane partitions). The variables correspond to a coloring of the boxes according to a finite Abelian subgroup $G$ of ${\rm SO}(3)$ . These generating functions turn out to be orbifold Donaldson-Thomas partition functions for the orbifold $[\mathbb{C}^3/G]$ . We need only the vertex operator methods of Okounkov, Reshetikhin, and Vafa for the easy case $G = \mathbb{Z}_n$ ; to handle the considerably more difficult case $G=\mathbb{Z}_2\times\mathbb{Z}_2$ , we 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 $[\mathbb{C}^3/G]$ . 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