Distribution of the sum of reciprocal parts for distinct parts partitions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912261146148864 |
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| author | Bridges, Walter |
| author_facet | Bridges, Walter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distribution of the sum of reciprocal parts for distinct parts partitions Bridges, Walter Number Theory Combinatorics Probability 11P82, 11D68, 60C05 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. |
| title | Distribution of the sum of reciprocal parts for distinct parts partitions |
| topic | Number Theory Combinatorics Probability 11P82, 11D68, 60C05 |
| url | https://arxiv.org/abs/2503.03899 |