  We calculate the partition function of a gas of particles obeying Haldane
exclusion statistics, using a definition of a Hilbert space having a
`fractional dimension' and constructing appropriate coherent states. The
fractional dimension is expressed though the form of the identity operator in
the Hilbert space. We find that there many possible generalisations of the
Pauli exclusion principle, with particular choices of the scalar product
leading to consistency either with Haldane's original definition of the
effective dimensionality of the Hilbert space or with the combinatorial
procedure invoked by Haldane and Wu. We explicitly demonstrate that at low
particle densities these definitions are equivalent.
