Integer partitions probability distributions

Abstract

Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in ${\mathbb{R}}^n$ obtained from the partitions of the fixed positive integer n. These distributions arise naturally when considering equally-likely random permutations on the set of n letters. For one of the distributions, the expectation vector and covariance matrix is derived. For the other distribution, conjectures for several elements of the expectation vector are provided.

Keywords:

• Integer partitions
• random partitions
• symmetric group
• discrete probability distribution

Acknowledgments

The author thanks Charles Champ, Dennis Eichhorn, Brandt Kronholm, Broderick Oluyede, and Robert Schneider for helpful conversations. The author thanks the referees for useful comments that have helped improve the exposition of this paper.