Year: 2024
Type: article
Abstract: 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.
Source: La Matematica
Authors: Lida Ahmadi, Ricardo Gómez-Aíza, Mark Daniel Ward
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funders: National Science Foundation, Eli Lilly and Company, Lilly Endowment, Society of Actuaries, Cummins Incorporated, Foundation for Food and Agriculture Research, National Institute of Food and Agriculture, Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México, Sandia National Laboratories
Awards: HDR DSC: National Data Mine Network, NSF Convergence Accelerator Track H: Developing Experiential Accessible Framework for Partnerships and Opportunities in Data Science (for the deaf community), G3254067602, HDR Institute: Geospatial Understanding through an Integrative Discovery Environment, Category I: Anvil - A National Composable Advanced Computational Resource for the Future of Science and Engineering, G3678507257, G5056912720, G5122199068, G5620962805, G5632484435, MCTP: Sophomore Transitions: Bridges into a Statistics Major and Big Data Research Experiences via Learning Communities, Emerging Frontiers of Science of Information, G7103612488, G8158425817, G8435054591, G923987444
OpenAlex ID: W4402259681