Integer Partitions Probability Distributions

12/11/2019

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by   Andrew V. Sills, et al.

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Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in 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.