Options
On the asymptotics of higher dimensional partitions
Date Issued
10-02-2012
Author(s)
Balakrishnan, Srivatsan
Indian Institute of Technology, Madras
Prabhakar, Naveen S.
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 provides some preliminary evidence for four- and five-dimensional partitions. © 2012 IOP Publishing Ltd.
Volume
45