On the smallest partition associated to a numerical semigroup
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913068360925184 |
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| author | Kaplan, Nathan Kim, Kaylee McGeorge, Cole Ramirez, Fabian Singhal, Deepesh |
| author_facet | Kaplan, Nathan Kim, Kaylee McGeorge, Cole Ramirez, Fabian Singhal, Deepesh |
| contents | The set of hook lengths of an integer partition $λ$ is the complement of some numerical semigroup $S$. There has been recent interest in studying the number of partitions with a given set of hook lengths. Very little is known about the distribution of sizes of this finite set of partitions. We focus on the problem of determining the size of the smallest partition with its set of hook lengths equal to $\mathbb{N}\setminus S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the smallest partition associated to a numerical semigroup Kaplan, Nathan Kim, Kaylee McGeorge, Cole Ramirez, Fabian Singhal, Deepesh Combinatorics 20M14, 05A17 The set of hook lengths of an integer partition $λ$ is the complement of some numerical semigroup $S$. There has been recent interest in studying the number of partitions with a given set of hook lengths. Very little is known about the distribution of sizes of this finite set of partitions. We focus on the problem of determining the size of the smallest partition with its set of hook lengths equal to $\mathbb{N}\setminus S$. |
| title | On the smallest partition associated to a numerical semigroup |
| topic | Combinatorics 20M14, 05A17 |
| url | https://arxiv.org/abs/2507.04169 |