On a problem involving unit fractions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916226216755200 |
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| author | Steinerberger, Stefan |
| author_facet | Steinerberger, Stefan |
| contents | Erdős and Graham proposed to determine the number of subsets $S \subseteq \left\{1,2,\dots,n\right\}$ with $\sum_{s \in S} 1/s = 1$ and asked, among other things, whether that number could be as large as $2^{n - o(n)}$. We show that the number of subsets $S \subseteq \left\{1,2,\dots,n\right\}$ with $\sum_{s \in S} 1/s \leq 1$ is smaller than $2^{0.93n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a problem involving unit fractions Steinerberger, Stefan Combinatorics Erdős and Graham proposed to determine the number of subsets $S \subseteq \left\{1,2,\dots,n\right\}$ with $\sum_{s \in S} 1/s = 1$ and asked, among other things, whether that number could be as large as $2^{n - o(n)}$. We show that the number of subsets $S \subseteq \left\{1,2,\dots,n\right\}$ with $\sum_{s \in S} 1/s \leq 1$ is smaller than $2^{0.93n}$. |
| title | On a problem involving unit fractions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.17041 |