  Let $K(q,t)= \|K_{\la\mu}(q,t)\|_{\la,\mu}$ be the Macdonald q,t-Kostka
matrix and $K(t)=K(0,t)$ be the matrix of the Kostka-Foulkes polynomials
K_{\la\mu}(t). In this paper we present a new proof of the polynomiality of the
q,t-Kostka coefficients that is both short and elementary. More precisely, we
derive that $K(q,t)$ has entries in \ZZ[q,t] directly from the fact that the
matrix $K(t)^{-1}$ has entries in \ZZ[t]. The proof uses only identities that
can be found in the original paper [7] of Macdonald.
