  We show that fractional exclusion statistics is manifested in general in
interacting systems and we discuss the conjecture recently introduced (J. Phys.
A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic
system the mutual exclusion statistics parameters are not zero, then they have
to be proportional to the dimension of the Hilbert space on which they act. By
using simple, intuitive arguments, but also concrete calculations in
interacting systems models, we show that this conjecture is not some abstract
consequence of unphysical modeling, but is a natural--and for a long time
overlooked--property of fractional exclusion statistics. We show also that the
fractional exclusion statistics is the consequence of interaction between the
particles of the system and it is due to the change from the description of the
system in terms of free-particle energies, to the description in terms of the
quasi-particle energies. From this result, the thermodynamic equivalence of
systems of the same, constant density of states, but any exclusion statistics
follows immediately.
