Partition functions and symmetric polynomials

Heinz-Jürgen Schmidt, Jürgen Schnack
2002 American Journal of Physics  
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
more » ... 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.
doi:10.1119/1.1412643 fatcat:nweaftqlnbe6jjzuztqrcnkzoi