  Inequalities are important features in the context of sequences of numbers
and polynomials. The Bessenrodt--Ono inequality for partition numbers and
Nekrasov--Okounkov polynomials has only recently been discovered. In this paper
we study the log-concavity (Tur\'{a}n inequality) and Bessenrodt--Ono
inequality for plane partitions and their polynomization.
