Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 13, No 1, (2000), 169p-172p
Abstract:
A partition of a positive integer n is a way of writing it as the sum of positive integers
without regard to order; the summands are called parts. The number of partitions of n,
usually denoted by p(n), is determined asymptotically by the famous partition formula
of Hardy and Ramanujan [5]. We shall introduce the uniform probability measure P on
the set of all partitions of n assuming that the probability 1/p(n) is assigned to each
n-partition. The symbols E and V ar will be further used to denote the expectation and
variance with respect to the measure P . Thus, each conceivable numerical characteristic
of the parts in a partition can be regarded as a random variable.
