High temperature expansion, Virial coefficients and Exclusion statistics

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We follow the generalisation of exclusion statistics to infinite dimensional Hilbert space as envisaged in Phys. Rev. Lett. 72, 3629, 1994. We reproduce the third virial coefficients at leading order for single species of anionic gas and 2nd mixed virial coefficients for multicomponent anionic gas. We argue that this particular method can be useful in determining definition of mutual exclusion statistics. We demonstrate this by taking high temperature expansion of two particle partition function of well known systems and show that it follows Haldane's definition of exclusion statistics. We also discuss equilibrium particle distributions at thermodynamic limit.