  We demonstrate an approach for exact sampling of certain discrete
combinatorial distributions, which is a hybrid of exact Boltzmann sampling and
the recursive method, using probabilistic divide-and-conquer (PDC). The
approach specializes to exact Boltzmann sampling in the trivial setting, and
specializes to PDC deterministic second half in the first non-trivial
application. A large class of examples is given for which this method broadly
applies, and several examples are worked out explicitly.
