关于高维分拆的渐近性
On the asymptotics of higher-dimensional partitions
摘要：
我们猜想立体（三维）划分数的渐近性态与三维MacMahon数的渐近性态是一致的。证据提供了一个确切的枚举固体分区的所有整数<=68，其号码是惊人的准确性使用渐近公式（与一个自由参数）和更好的精度增加的自由参数。我们还推测，类似的行为举行高维分区，并提供了一些初步的证据，四维和五维分区。
英文摘要：
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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