Fractional exclusion statistics as an occupancy process

Abstract

We show the possibility of describing fractional exclusion statistics (FES) as an occupancy process with global and local exclusion constraints. More specifically, using combinatorial identities, we show that FES can be viewed as “ball-in-box” models with appropriate weighting on the set of occupancy configurations (merely represented by a partition of the total number of particles). As a consequence, the following exact statement of the generalized Pauli principle is derived: for an [Formula: see text]-particles system exhibiting FES of extended parameter [Formula: see text] ([Formula: see text] and [Formula: see text] are co-prime integers such that [Formula: see text]), (1) the allowed occupation number of a state is less than or equal to [Formula: see text] and not to [Formula: see text] whenever [Formula: see text] and (2) the global occupancy shape is admissible if the number of states occupied by at least two particles is less than or equal to [Formula: see text] ([Formula: see text]). These counting rules allow distinguishing infinitely many families of FES systems depending on the parameter [Formula: see text] and the size [Formula: see text].