2025/09/26 by A. David Christopher, Christopher, A. David
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Analytic Number Theory Research
paper · pdf · doi:10.48550/arxiv.2509.22618
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.