A Unified Treatment of Families of Partition Functions

Author:

Ahmadi Lida,Gómez-Aíza RicardoORCID,Ward Mark Daniel

Abstract

AbstractWe 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.

Funder

Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México

National Science Foundation

Foundation for Food and Agriculture Research

National Institute of Food and Agriculture

Society of Actuaries

Cummins Incorporated

Gro Master

Lilly Endowment

Sandia National Laboratories

Publisher

Springer Science and Business Media LLC

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