  By taking the freezing limit of a spin Calogero-Sutherland model containing
`anyon like' representation of the permutation algebra, we derive the exact
partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain.
This partition function allows us to study global properties of the spectrum
like level density distribution and nearest neighbour spacing distribution. It
is found that, for supersymmetric HS spin chains with large number of lattice
sites, continuous part of the energy level density obeys Gaussian distribution
with a high degree of accuracy. The mean value and standard deviation of such
Gaussian distribution can be calculated exactly. We also conjecture that the
partition function of supersymmetric HS spin chain satisfies a duality relation
under the exchange of bosonic and fermionic spin degrees of freedom.
