Optimal transport and integer partitions

Sonja Hohloch

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arXiv · 1704.01666

Optimal transport and integer partitions

Sonja Hohloch

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Abstract

We link the theory of optimal transportation to the theory of integer partitions. Let $\mathscr P(n)$ denote the set of integer partitions of $n \in \mathbb N$ and write partitions $\pi \in \mathscr P(n)$ as $(n_1, \dots, n_{k(\pi)})$. Using terminology from optimal transport, we characterize certain classes of partitions like symmetric partitions and those in Euler's identity $|\{ \pi \in \mathscr P(n) |$ all $ n_i $ distinct $ \} | = | \{ \pi \in \mathscr P(n) | $ all $ n_i $ odd $ \}|$. Then we sketch how optimal transport might help to understand higher dimensional partitions.

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BibTeX RIS

Sonja Hohloch. 2017-04-05. Optimal transport and integer partitions. https://arxiv.org/abs/1704.01666

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