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

TL;DR

This paper establishes criteria for log-concavity and strong q-log-convexity in generalized triangular arrays, and proves that the bi^s-nomial transformation preserves these properties, advancing understanding of their combinatorial structures.

Contribution

It introduces new criteria for log-concavity and strong q-log-convexity in generalized triangles and shows the bi^s-nomial transformation preserves these properties.

Findings

Criteria for log-concavity of rows in generalized triangles

Criteria for strong q-log-convexity of generating functions

Bi^s-nomial transformation preserves both properties

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.