Fixed perimeter analogues of some partition results
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916619131813888 |
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| author | Gray, Gabriel Payne, Emily Swisher, Holly Watson, Ren |
| author_facet | Gray, Gabriel Payne, Emily Swisher, Holly Watson, Ren |
| contents | Euler's partition identity states that the number of partitions of $n$ into odd parts is equal to the number of partitions of $n$ into distinct parts. Strikingly, Straub proved in 2016 that this identity also holds when counting partitions of any size with largest hook (perimeter) $n$. This has inspired further investigation of partition identities and inequalities in the fixed perimeter setting. Here, we explore fixed perimeter analogues of some well-known partition results inspired by Euler's partition identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed perimeter analogues of some partition results Gray, Gabriel Payne, Emily Swisher, Holly Watson, Ren Combinatorics Number Theory 05A17, 05A19, 11P81, 11P84 Euler's partition identity states that the number of partitions of $n$ into odd parts is equal to the number of partitions of $n$ into distinct parts. Strikingly, Straub proved in 2016 that this identity also holds when counting partitions of any size with largest hook (perimeter) $n$. This has inspired further investigation of partition identities and inequalities in the fixed perimeter setting. Here, we explore fixed perimeter analogues of some well-known partition results inspired by Euler's partition identity. |
| title | Fixed perimeter analogues of some partition results |
| topic | Combinatorics Number Theory 05A17, 05A19, 11P81, 11P84 |
| url | https://arxiv.org/abs/2502.12394 |