  Plane partitions naturally appear in many problems of statistical physics and
quantum field theory, for instance, in the theory of faceted crystals and of
topological strings on Calabi-Yau threefolds. In this paper a connection is
made between the exactly solvable model with the boson dynamical variables and
a problem of enumeration of boxed plane partitions - three dimensional Young
diagrams placed into a box of a finite size. The correlation functions of the
boson model may be considered as the generating functionals of the Young
diagrams with the fixed heights of its certain columns. The evaluation of the
correlation functions is based on the Yang-Baxter algebra. The analytical
answers are obtained in terms of determinants and they can also be expressed
through the Schur functions.
