2023/03/03 by Lida Ahmadi, Ahmadi, Lida, Ricardo Gómez Aíza +3
Mathematics · #05A15 #05A16 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2303.02240
openalex publication_date 2023/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a unified framework of combinatorial descriptions, and the analogous asymptotic growth of the coefficients of two general families of functions related to integer partitions. In particular, we resolve several conjectures and verify several claims that are posted on the On-Line Encyclopedia of Integer Sequences. We perform the asymptotic analysis by systematically applying the Mellin transform, residue analysis, and the saddle point method. The combinatorial descriptions of these families of generalized partition functions involve colorings of Young tableaux, along with their ``divisor diagrams'', denoted with sets of colors whose sizes are controlled by divisor functions.