New inequalities for \(p(n)\) and \(\log p(n)\) (Q6164978)

For the partition function \(p(n)\), the authors provide an infinite family of inequalities which generalizes a result by \textit{W. Y. C. Chen} et al. [Trans. Am. Math. Soc. 372, No. 3, 2143--2165 (2019; Zbl 1415.05020)]. They consider this new infinite family of inequalities in order to derive an infinite family of inequalities for \(\log p(n)\). Some applications of this result are presented in this context.