A note on the number of partitions of $n$ into $k$ parts
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913334568157184 |
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| author | Cimpoeas, Mircea |
| author_facet | Cimpoeas, Mircea |
| contents | We prove new formulas and congruences for $p(n,k):=$ the number of partitions of $n$ into $k$ parts and $q(n,k):=$ the number of partitions of $n$ into $k$ distinct parts. Also, we give lower and upper bounds for the density of the set $\{n\in\mathbb N\;:\;p(n,k)\equiv i(\bmod\; m)\}$, where $m\geq 2$ and $0\leq i\leq m-1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2111_00914 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A note on the number of partitions of $n$ into $k$ parts Cimpoeas, Mircea Combinatorics Number Theory 11P81, 11P83 We prove new formulas and congruences for $p(n,k):=$ the number of partitions of $n$ into $k$ parts and $q(n,k):=$ the number of partitions of $n$ into $k$ distinct parts. Also, we give lower and upper bounds for the density of the set $\{n\in\mathbb N\;:\;p(n,k)\equiv i(\bmod\; m)\}$, where $m\geq 2$ and $0\leq i\leq m-1$. |
| title | A note on the number of partitions of $n$ into $k$ parts |
| topic | Combinatorics Number Theory 11P81, 11P83 |
| url | https://arxiv.org/abs/2111.00914 |