Distribution of the sum of reciprocal parts for distinct parts partitions

Walter Bridges

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arXiv · 2503.03899

Distribution of the sum of reciprocal parts for distinct parts partitions

Walter Bridges

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Abstract

Given an integer partition of $n$ into distinct parts, the sum of the reciprocal parts is an example of an egyptian fraction. We study this statistic under the uniform measure on distinct parts partitions of $n$ and prove that, as $n \to \infty$, the sum of reciprocal parts is distributed away from its mean like a random harmonic sum.

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Walter Bridges. 2025-03-05. Distribution of the sum of reciprocal parts for distinct parts partitions. https://arxiv.org/abs/2503.03899

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