On the asymptotics of higher-dimensional partitions

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.

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

References in corpus (3)

• Counting Gauge Invariants: the Plethystic Program
• Motivic degree zero Donaldson-Thomas invariants
• Asymptotic counting of BPS operators in superconformal field theories

Cited by in corpus (6)

• Partition Functions for Higher-Spin theories in AdS
• Estimating the asymptotics of solid partitions
• Notes on higher-dimensional partitions
• The motive of the Hilbert scheme of points in all dimensions
• On the cardinality of lower sets and universal discretization
• Bounds for the number of multidimensional partitions