Integer Partitions and Exclusion Statistics

TL;DR

This paper explores the combinatorial structure of exclusion statistics through minimal difference partitions, revealing that the distribution of parts transitions from Gumbel to Gaussian as the parameter p varies.

Contribution

It provides a novel combinatorial framework for understanding exclusion statistics using minimal difference partitions and characterizes the limiting distributions for different p values.

Findings

At p=0, the distribution is Gumbel, indicating a repulsive fixed point.

For all positive p, the distribution converges to a Gaussian form.

The probability distribution of the number of parts is explicitly computed for random minimal p partitions.

Abstract

We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $ p=0$ is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive $p$ the distribution is shown to be Gaussian.