The partition function for "composite particles"

We calculate the partition function for "composite particles". For any finite number of states d, and in the following two cases: 1)all states have the same energy, 2)the energy is linearly distributed over the states, we transform the partition function into a finite sum of terms which exhibit trivially their $% d $dependance. The infinite d thermodynamic limit is obtained as well as the finite d-size corrections, etc. In the second case, we obtain the finite d-size corrections to "the universal chiral partition function for exclusion statistics".