An investigation of a certain class of approximate solutions of the Yvonhyphen;Bornhyphen;Green recurrence relations for the lowerhyphen;dimensional molecular distribution functions has been presented, based on a particular mechanism of exclusion of interactions among ``clusters'' composed of successively larger number of molecules. This mechanism leads to a chain of equations for the approximate distribution functions which (a) converge to the exact molecular distribution function after a finite number of approximations, (b) are linear in the dependent variable just like the Yvonhyphen;Bornhyphen;Green recurrence relations, and (c) are time reversible. The connection between these equations and certain natural generalizations of Boltzmann's equation to other than binary collisions is obtained. Finally the application of this hierarchy to certain problems of fluids at equilibrium has been indicated.
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