Asymptotics of the number partitioning distribution
Abstract
Description
The number partitioning problem can be interpreted physically in terms of a thermally isolated non-interacting Bose gas trapped in a one-dimensional harmonic oscillator potential. We exploit this analogy to characterize, by means of a detour to the Bose gas within the canonical ensemble, the probability distribution for finding a specified number of summands in a randomly chosen partition of an integer n. It is shown that this distribution approaches its asymptotics only for n > 10^10.
to appear in Europhysics Letters http://www.edpsciences.com/euro/
to appear in Europhysics Letters http://www.edpsciences.com/euro/