  We study exclusion statistics within the second quantized approach. We
consider operator algebras with positive definite Fock space and restrict them
in a such a way that certain state vectors in Fock space are forbidden ab
initio.We describe three characteristic examples of such exclusion, namely
exclusion on the base space which is characterized by states with specific
constraint on quantum numbers belonging to base space M (e.g.
Calogero-Sutherland type of exclusion statistics), exclusion in the
single-oscillator Fock space, where some states in single oscillator Fock space
are forbidden (e.g. the Gentile realization of exclusion statistics) and a
combination of these two exclusions (e.g. Green's realization of para-Fermi
statistics). For these types of exclusions we discuss extended Haldane
statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A
11, 3081 (1996), and associated counting rules. Within these three types of
exclusions in Fock space the original Haldane exclusion statistics cannot be
realized.
