Inequalities for Plane Partitions

TL;DR

This paper investigates inequalities such as log-concavity and Bessenrodt--Ono for plane partitions and their polynomials, expanding understanding of their mathematical properties.

Contribution

It introduces new results on inequalities for plane partitions and their polynomization, extending recent discoveries in partition number inequalities.

Findings

Establishes log-concavity (Turán inequality) for plane partitions.

Proves Bessenrodt--Ono inequality for plane partitions.

Analyzes inequalities for polynomized plane partitions.

Abstract

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.