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)

Publisher: Springer

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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: ljuben@nws.aubg.bg

Publication date: January 1, 2000

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