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Tuesday, March 10, 2015

**Abstract:** Although MacMahon’s conjecture about the generating function for multidimensional partitions was disproved by Atkin, et al. in 1967, there has been renewed interest in the asymptotic accuracy of this conjecture among physicists since the mid 1990s. Many of the resulting publications are computational in nature, providing very suggestive data. Others make headway in rigorously establishing the asymptotics of the number of multidimensional partitions. The best known result is that $\log p_d(n)$ is asymptotically equivalent to $n^{d/(d+1)}$.