On the asymptotics of higher dimensional partitions

2011/05/31 by Srivatsan Balakrishnan, Suresh Govindarajan, Naveen S. Prabhakar
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematics #cond-mat.stat-mech #hep-th #math.CO

paper · pdf · doi:10.1088/1751-8113/45/5/055001

published as J.Phys.A A45 (2012) 055001 · 30 pages, 8 tables, 4 figures (v2) New data (63-68) for solid partitions added; (v3) published version, new subsection providing an unbiased estimate of the leading for the leading coefficient added, some tables deleted

arxiv created 2011/12/09 · openalex publication_date 2012/01/12 · arxiv updated 2012/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We conjecture that the asymptotic behavior of the numbers of solid (three-dimensional) partitions is identical to the asymptotics of the three-dimensional MacMahon numbers. Evidence is provided by an exact enumeration of solid partitions of all integers <=68 whose numbers are reproduced with surprising accuracy using the asymptotic formula (with one free parameter) and better accuracy on increasing the number of free parameters. We also conjecture that similar behavior holds for higher-dimensional partitions and provide some preliminary evidence for four and five-dimensional partitions.

Citations

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