Partitions with Durfee triangles of fixed size
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913959740702720 |
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| author | Sharan, N. Guru Straub, Armin |
| author_facet | Sharan, N. Guru Straub, Armin |
| contents | A well-studied statistic of an integer partition is the size of its Durfee square. In particular, the number $D_k (n)$ of partitions of $n$ with Durfee square of fixed size $k$ has a well-known simple rational generating function. We study the number $R_k (n)$ of partitions of $n$ with Durfee triangle of size $k$ (the largest subpartition with parts $1, 2, \ldots, k$). We determine the corresponding generating functions which are rational functions of a similar form. Moreover, we explicitly determine the leading asymptotic of $R_k (n)$, as $n \rightarrow \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19047 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partitions with Durfee triangles of fixed size Sharan, N. Guru Straub, Armin Combinatorics Number Theory Primary 05A17 A well-studied statistic of an integer partition is the size of its Durfee square. In particular, the number $D_k (n)$ of partitions of $n$ with Durfee square of fixed size $k$ has a well-known simple rational generating function. We study the number $R_k (n)$ of partitions of $n$ with Durfee triangle of size $k$ (the largest subpartition with parts $1, 2, \ldots, k$). We determine the corresponding generating functions which are rational functions of a similar form. Moreover, we explicitly determine the leading asymptotic of $R_k (n)$, as $n \rightarrow \infty$. |
| title | Partitions with Durfee triangles of fixed size |
| topic | Combinatorics Number Theory Primary 05A17 |
| url | https://arxiv.org/abs/2507.19047 |