Counting subsets of the random partition and the 'Brownian Bridge' process

Let [Omega]m be the set of partitions, [omega], of a finite m-element set; induce a uniform probability distribution on [Omega]m, and define Xms([omega]) as the number of s-element subsets in [omega]. We alow the existence of an integer-valued function n=n(m)(t), t[epsilon][0, 1], and centering constants bms, 0[less-than-or-equals, slant]s[less-than-or-equals, slant] m, such that converges to the 'Brownian Bridge' process in terms of its finite-dimensional distributions.