Integer Partitions and Exclusion Statistics

Alain Comtet ^1, 2, Satya N. Majumdar ¹, Stephane Ouvry ¹

Journal of Physics A General Physics 40 (2007) 11255-11269

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.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 2. IHP,
  Institut Henri Poincaré