Cumulants of partitions

Abstract

We utilize the formal equivalence between the number-partitioning problem and a harmonically trapped ideal Bose gas within the microcanonical ensemble for characterizing the probability distribution which governs the number of addends occurring in an unrestricted partition of a natural number n. By deriving accurate asymptotic formulae for its coefficients of skewness and excess, it is shown that this distribution remains non-Gaussian even when n is made arbitrarily large. Both skewness and excess vary substantially before settling to their constant-limiting values for n > 1010.