  A general formula for the canonical partition function for a system obeying
any statistics based on the permutation group is derived. The formula expresses
the canonical partition function in terms of sums of Schur functions. The only
hitherto known result due to Suranyi [ Phys. Rev. Lett. {\bf 65}, 2329 (1990)]
for parasystems of order two is shown to arise as a special case of our general
formula. Our results also yield all the relevant information about the
structure of the Fock spaces for parasystems.
