Asymptotics of the number partitioning distribution

Details Asymptotics of the number partitioning distribution Asymptotics of the number partitioning distribution

2002-06-03

arxiv.org/abs/cond-mat/0206023v1

Europhys. Lett. 59, 486 (2002)

Physics

Condensed Matter

Statistical Mechanics

to appear in Europhysics Letters http://www.edpsciences.com/euro/

Scientific paper

10.1209/epl/i2002-00133-6

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.

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