Laguerre inequalities for plane partition

Abstract

In this paper, we establish the Laguerre inequalities of order 2 and 3 for the number of plane partition $\mathrm{PL}\left(n\right)$. We also demonstrate that $\mathrm{PL}\left(n\right)$ satisfies the double Turán inequality. Moreover, we give an upper bound for the threshold of the Laguerre inequality of any order $r>3$ for $\mathrm{PL}\left(n\right)$.