Showing papers by "Suresh Govindarajan published in 2015"

Estimating the Asymptotics of Solid Partitions

Abstract: We study the asymptotic behavior of solid partitions using transition matrix Monte Carlo simulations. If $$p_3(n)$$ denotes the number of solid partitions of an integer $$n$$ , we show that $$\lim _{n\rightarrow \infty } n^{-3/4} \log p_3(n)\sim 1.822\pm 0.001$$ . This shows clear deviation from the value $$1.7898$$ , attained by MacMahon numbers $$m_3(n)$$ , that was conjectured to hold for solid partitions as well. In addition, we find estimates for other sub-leading terms in $$\log p_3(n)$$ . In a pattern deviating from the asymptotics of line and plane partitions, we need to add an oscillatory term in addition to the obvious sub-leading terms. The period of the oscillatory term is proportional to $$n^{1/4}$$ , the natural scale in the problem. This new oscillatory term might shed some insight into why partitions in dimensions greater than two do not admit a simple generating function.