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We study exclusion statistics within the second quantized approach. Weconsider operator algebras with positive definite Fock space and restrict themin a such a way that certain state vectors in Fock space are forbidden abinitio.We describe three characteristic examples of such exclusion, namelyexclusion on the base space which is characterized by states with specificconstraint on quantum numbers belonging to base space M (e.g.Calogero-Sutherland type of exclusion statistics), exclusion in thesingle-oscillator Fock space, where some states in single oscillator Fock spaceare forbidden (e.g. the Gentile realization of exclusion statistics) and acombination of these two exclusions (e.g. Green's realization of para-Fermistatistics). For these types of exclusions we discuss extended Haldanestatistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A11, 3081 (1996), and associated counting rules. Within these three types ofexclusions in Fock space the original Haldane exclusion statistics cannot berealized.Comment: Latex,31 pages,no figures,to appear in J.Phys.A : Math.Ge

Exclusion statistics, operator algebras and Fock space representations