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  • 1 American University in Bulgaria 2700 Blagoevgrad Bulgaria E-mail
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Abstract  

Let Ys,n denote the number of part sizes ≧ s in a random and uniform partition of the positive integer n that are counted without multiplicity. For s = λ(6n)1/2/π + o(n1/4), 0 ≦ λ < ∞, as n → ∞, we establish the weak convergence of Ys,n to a Gaussian distribution in the form of a central limit theorem. The mean and the standard deviation are also asymptotically determined.

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