Asymptotics of the number partitioning distribution
Fachbereich Physik, Carl von Ossietzky Universität -
D-26111 Oldenburg, Germany
Accepted: 16 May 2002
The number partitioning problem can be interpreted physically in terms of a thermally isolated noninteracting 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 .
PACS: 05.30.Ch – Quantum ensemble theory / 05.30.Jp – Boson systems / 02.30.Mv – Approximations and expansions
© EDP Sciences, 2002