  MacMahon's classic generating function of random plane partitions, which is
related to Schur polynomials, was recently extended by Vuletic to a generating
function of weighted plane partitions that is related to Hall-Littlewood
polynomials, S(t), and further to one related to Macdonald polynomials, S(t,q).
  Using Jing's 1-parameter deformation of charged free fermions, we obtain a
Fock space derivation of the Hall-Littlewood extension. Confining the plane
partitions to a finite s-by-s square base, we show that the resulting
generating function, S_{s-by-s}(t), is an evaluation of a tau-function of KP.
