On the asymptotics of higher-dimensional partitions

Details On the asymptotics of higher-dimensional partitions On the asymptotics of higher-dimensional partitions

2011-05-31

arxiv.org/abs/1105.6231v3

J.Phys.A A45 (2012) 055001

Physics

Condensed Matter

Statistical Mechanics

30 pages, 8 tables, 4 figures (v2) New data (63-68) for solid partitions added; (v3) published version, new subsection providi

Scientific paper

10.1088/1751-8113/45/5/055001

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.

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