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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.22618 |
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| _version_ | 1866918148979032064 |
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| author | Christopher, A. David |
| author_facet | Christopher, A. David |
| contents | The number of parts in the partitions (resp. distinct partitions) of $n$ with parts from a set were considered. Its generating functions were obtained. Consequently, we derive several recurrence identities for the following functions: the number of prime divisors of $n$, $p$-adic valuation of $n$, the number of Carlitz-binary compositions of $n$ and the Hamming weight function. Finally, we obtain an asymptotic estimate for the number of parts in the partitions of $n$ with parts from a finite set of relatively prime integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Number of Parts in the (Distinct) Partitions With Parts From a Set Christopher, A. David Number Theory The number of parts in the partitions (resp. distinct partitions) of $n$ with parts from a set were considered. Its generating functions were obtained. Consequently, we derive several recurrence identities for the following functions: the number of prime divisors of $n$, $p$-adic valuation of $n$, the number of Carlitz-binary compositions of $n$ and the Hamming weight function. Finally, we obtain an asymptotic estimate for the number of parts in the partitions of $n$ with parts from a finite set of relatively prime integers. |
| title | The Number of Parts in the (Distinct) Partitions With Parts From a Set |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.22618 |