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Asymptotics of the number partitioning distribution

C. Weiss·M. Holthaus
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Abstract

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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C. Weiss, M. Holthaus. 2002-06-03. Asymptotics of the number partitioning distribution. https://doi.org/10.1209/epl%2Fi2002-00133-6

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