Large Distinct Part Sizes in a Random Integer Partition
Author: Mutafchiev, L.R.
Source: Acta Mathematica Hungarica, Volume 87, Numbers 1-2, 2000 , pp. 47-69(23)
Abstract:Let Y_s,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 = (6n)^1/2/ + o(n^1/4), 0 ≦ < ∞, as n → ∞, we establish the weak convergence of Y_s,n to a Gaussian distribution in the form of a central limit theorem. The mean and the standard deviation are also asymptotically determined.
Document Type: Regular Paper
Affiliations: American University in Bulgaria 2700 Blagoevgrad Bulgaria E-mail: firstname.lastname@example.org
Publication date: January 1, 2000