Enumerative Properties of NC (B) (p,q)

We determine the rank generating function, the zeta polynomial and the Mobius function for the poset NC(B)(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We give an alternative treatment of some of these results in the case q = 1, for which this poset is a lattice. We also consider the general case of multiannular noncrossing partitions of type B, and prove that this reduces to the cases of non-crossing partitions of type B in the annulus and the disc.