Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.22618 |
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Sommario:
- 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.