Log-concavity and strong $q$-log-convexity for some generalized triangular arrays

Abstract

In this paper, we provide criteria for the log-concavity of rows and the strong $q$-log-convexity of the generating functions of rows in more generalized triangles. Additionally, we prove that the bi${}^s$nomial transformation not only preserves the strong $q$-log-convexity property but also preserves the strong $q$-log-concavity property.