Combinatorial Proof of a Partition Inequality of Bessenrodt-Ono

We provide a combinatorial proof of the inequality p(a)p(b)>p(a+b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p(a)p(b) > p(a+b)}$$\end{document}, where p(n) is the partition function and a, b>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${b > 1}$$\end{document} are integers satisfying a+b>9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a+b > 9}$$\end{document}. This problem was posed by Bessenrodt and Ono who used the inequality to study a new multiplicative property of an extended partition function [Ann. Combin. 20, 59–64 (2016)].