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arXiv · 1912.00575

Nuclear partitions and a formula for $p(n)$

Robert Schneider
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Abstract

Define a "nuclear partition" to be an integer partition with no part equal to one. In this study we prove a simple formula to compute the partition function $p(n)$ by counting only the nuclear partitions of $n$, a vanishingly small subset by comparison with all partitions of $n$ as $n\to \infty$. Variations on the proof yield other formulas for $p(n)$, as well as Ramanujan-like congruences and an application to parity of the partition function.

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Robert Schneider. 2019-12-02. Nuclear partitions and a formula for $p(n)$. https://arxiv.org/abs/1912.00575

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