A note on the number of plane partitions and $r$-component multipartitions of $n$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911876427808768 |
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| author | Cimpoeas, Mircea Teodor, Alexandra |
| author_facet | Cimpoeas, Mircea Teodor, Alexandra |
| contents | Using elementary methods, we prove new formulas for $\operatorname{pp}(n)$, the number of plane partitions of $n$, $\operatorname{pp}_r(n)$, the number of plane partitions of $n$ with at most $r$ rows, $\operatorname{pp}^s(n)$, the number of strict plane partitions of $n$ and $\operatorname{pp}^{so}(n)$, the number of symmetric plane partitions of $n$. Also, we give new formulas for $P_r(n)$, the number of $r$-component multipartitions of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the number of plane partitions and $r$-component multipartitions of $n$ Cimpoeas, Mircea Teodor, Alexandra Combinatorics 11P81, 11P83 Using elementary methods, we prove new formulas for $\operatorname{pp}(n)$, the number of plane partitions of $n$, $\operatorname{pp}_r(n)$, the number of plane partitions of $n$ with at most $r$ rows, $\operatorname{pp}^s(n)$, the number of strict plane partitions of $n$ and $\operatorname{pp}^{so}(n)$, the number of symmetric plane partitions of $n$. Also, we give new formulas for $P_r(n)$, the number of $r$-component multipartitions of $n$. |
| title | A note on the number of plane partitions and $r$-component multipartitions of $n$ |
| topic | Combinatorics 11P81, 11P83 |
| url | https://arxiv.org/abs/2402.00660 |