  The thermodynamic properties of bosons moving in a harmonic trap in an
arbitrary number of dimensions are investigated in the grand canonical,
canonical and microcanonical ensembles by applying combinatorial techniques
developed earlier in statistical nuclear fragmentation models. Thermodynamic
functions such as the energy and specific heat are computed exactly in these
ensembles. The occupation of the ground or condensed state is also obtained
exactly, and signals clearly the phase transition. The application of these
techniques to fermionic systems is also briefly discussed.
