Sharp Bounds for Sets with Distinct Subset Products
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917297590894592 |
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| author | Raghavan, Rushil |
| author_facet | Raghavan, Rushil |
| contents | Let $A\subseteq [N]$ be such that for any pair of distinct subsets $B,C\subset A$, the products $\prod_{b\in B}b$ and $\prod_{c\in C}c$ are distinct. We prove that $|A|\leq π(N)+π(N^{1/2})+o(π(N^{1/2}))$, where $π$ is the prime counting function, answering a question of Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Bounds for Sets with Distinct Subset Products Raghavan, Rushil Combinatorics Number Theory 11B75 Let $A\subseteq [N]$ be such that for any pair of distinct subsets $B,C\subset A$, the products $\prod_{b\in B}b$ and $\prod_{c\in C}c$ are distinct. We prove that $|A|\leq π(N)+π(N^{1/2})+o(π(N^{1/2}))$, where $π$ is the prime counting function, answering a question of Erdős. |
| title | Sharp Bounds for Sets with Distinct Subset Products |
| topic | Combinatorics Number Theory 11B75 |
| url | https://arxiv.org/abs/2501.02695 |