The orbifold DT/PT vertex correspondence

We present an orbifold topological vertex formalism for PT invariants of toric Calabi-Yau 3-orbifolds with transverse $A_{n-1}$ singularities. We give a proof of the orbifold DT/PT Calabi-Yau topological vertex correspondence. As an application, we derive an explicit formula for the PT $\mathbb{Z}_{n}$-vertex in terms of loop Schur functions and prove the multi-regular orbifold DT/PT correspondence.