  We find a close correspondence between certain partition functions of ideal
quantum gases and certain symmetric polynomials. Due to this correspondence it
can be shown that a number of thermodynamic identities which have recently been
considered are essentially of combinatorical origin and known for a long time
as theorems on symmetric polynomials. For example, a recurrence relation for
partition functions appearing in the textbook of P. Landsberg is nothing else
but Newton's identity in disguised form. Conversely, a certain theorem on
symmetric polynomials translates into a new and unexpected relation between
fermionic and bosonic partition functions, which can be used to express the
former by means of the latter and vice versa.
