Some inequalities for \(k\)-colored partition functions (Q1656807)

In this paper, the authors acquire partition inequalities for \(k\)-colored partition functions \(p_-k(n)\) for all \(k>3\), which are analogues to the partition inequality given by \textit{C. Bessenrodt} and \textit{K. Ono} [Ann. Comb. 20, No. 1, 59--64 (2016; Zbl 1332.05013)]. By means of these inequalities, they consider to extend the \(k\)-colored partition function multiplicatively to a function on a \(k\)-colored partition and also characterize when it has a unique maximum. To strengthen the foregoing result, they provide a conjectural inequality.