Total positivity of Riordan arrays

TL;DR

This paper establishes conditions under which Riordan arrays are totally positive, demonstrating that many classical combinatorial triangles possess this property and that numerous well-known combinatorial numbers are log-convex.

Contribution

It provides a unified framework for proving total positivity of Riordan arrays and related combinatorial numbers, expanding understanding of their structural properties.

Findings

Many classical combinatorial triangles are totally positive.

Numerous combinatorial numbers are shown to be log-convex.

The paper offers sufficient conditions for total positivity in Riordan arrays.

Abstract

We present sufficient conditions for total positivity of Riordan arrays. As applications we show that many well-known combinatorial triangles are totally positive and many famous combinatorial numbers are log-convex in a unified approach.