Integer Partitions and Exclusion Statistics
arXiv:0705.2640 · doi:10.1088/1751-8113/40/37/004
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.
16 pages, 4 .eps figures included