A generalization of Franklin's partition identity and a Beck-type companion identity
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866912082496061440 |
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| author | Gray, Gabriel Hovey, David Kronholm, Brandt Payne, Emily Swisher, Holly Watson, Ren |
| author_facet | Gray, Gabriel Hovey, David Kronholm, Brandt Payne, Emily Swisher, Holly Watson, Ren |
| contents | Euler's classic partition identity states that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We develop a new generalization of this identity, which yields a previous generalization of Franklin as a special case, and prove an accompanying Beck-type companion identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalization of Franklin's partition identity and a Beck-type companion identity Gray, Gabriel Hovey, David Kronholm, Brandt Payne, Emily Swisher, Holly Watson, Ren Number Theory Combinatorics Euler's classic partition identity states that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We develop a new generalization of this identity, which yields a previous generalization of Franklin as a special case, and prove an accompanying Beck-type companion identity. |
| title | A generalization of Franklin's partition identity and a Beck-type companion identity |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2410.17378 |