Asymptotic counting of BPS operators in superconformal field theories

We consider some aspects of counting BPS operators which are annihilated by two supercharges in superconformal field theories. For nonzero coupling, the corresponding multivariable partition functions can be written in terms of generating functions for vector partitions or their weighted generalizations. We derive asymptotics for the density of states for a wide class of such multivariable partition functions. We also point out a particular factorization property of the finite N partition functions. Finally, we discuss the concept of a limit curve arising from the large N partition functions, which is related to the notion of a "typical state," and discuss some implications for the holographic duals.