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A partition function computes the number of ways an integer $n$ can be represented as the sum of $m$ other integers. For some value $n$, we have a partition function $p(n)$.

These were studied extensively in mathematics by MacMahon, Hardy, Littlewood and Ramanujan. Rademacher provided a way to approximating $p(n)$, improving on a formula by hardy and Littlewood. More recently, K. Ono and A. Wiles have come up with new interesting results.

Are there applications of partition functions in Computer Sciences, perhaps in the theory of elliptic curve cryptography or complexity?

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  • $\begingroup$ Definitely not in elliptic curve cryptography. $\endgroup$ – Yuval Filmus Aug 9 '14 at 2:46
  • $\begingroup$ They might come in algorithm analysis, sure. $\endgroup$ – Raphael Aug 9 '14 at 12:21
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