A Unified Treatment of Families of Partition Functions
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.
Authors
- Lida Ahmadi (ORCID: https://orcid.org/0000-0002-9017-4359)
- Mark Daniel Ward (ORCID: https://orcid.org/0000-0001-8795-746X)
- Ricardo Gómez Aíza (ORCID: https://orcid.org/0000-0002-2614-8519)
Institutions
- Purdue University West Lafayette (US)
- California State University, San Bernardino (US)
- Universidad Nacional Autónoma de México (MX)
Publication Details
- Journal
- La Matematica
- Published
- 2024-09-05
- DOI
- https://doi.org/10.1007/s44007-024-00134-w
- Citations
- 2
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 2.54
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