Optimal transport and integer partitions

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Abstract

We link the theory of optimal transportation to the theory of integer partitions. Let P(n) denote the set of integer partitions of n εN and write partitions π εP(n) as (<sup>n1</sup>,...,nk(<inf>π)</inf>). Using terminology from optimal transport, we characterize certain classes of partitions like symmetric partitions and those in Euler's identity|{π εP(n) all <sup>ni</sup> distinct}|=|{π εP(n) all <sup>ni</sup> odd}|. Then we sketch how optimal transport might help to understand higher dimensional partitions.

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APA

Hohloch, S. (2015). Optimal transport and integer partitions. Discrete Applied Mathematics, 190191, 75–85. https://doi.org/10.1016/j.dam.2015.04.002

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