Inequalities for Plane Partitions

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.