2018/07/29 by Nour-Eddine Fahssi, Fahssi, Nour-Eddine
Mathematics · #05A10 #05A17 #05A19 #82-XX #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1808.00045
openalex publication_date 2018/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is a revision of the combinatorics of fractional exclusion statistics (FES). More specifically, the following exact statement of the generalized Pauli principle is derived: for an N-particles system exhibiting FES of extended parameter g=q/r (q and r are co-prime integers such that 0 < q ≤ r), we found that the allowed occupation number of a state is smaller than or equal to r-q+1 and not to 1/g whenever q≠ 1 and, moreover, the global occupancy shape (merely represented by a partition of N) is admissible if the number of states occupied by at least two particles is less than or equal to (N-1)/r (N ≡ 1 \pmod r). These counting rules allow distinguishing infinitely many families of FES systems depending on the parameter g and the size N. As an application of the main result, we study the probability distributions of occupancy configurations. For instance, the number of occupied states is found to be a hypergeometric random variable. Closed-form expressions for the expectation values and variances in the thermodynamic limit are presented. By way of comparison, we obtain parallel results regarding the Gentile intermediate statistics and demonstrate subtle similarities and contrasts with respect to FES.