Journal of Integer Sequences, Vol. 28 (2025), Article 25.7.5

A New Criterion for the Total Positivity of Riordan Arrays


Lili Mu
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, 221116
PR China

Yuanyuan Xing
School of Mathematics
Liaoning Normal University
Dalian, 116029
PR China

Sai-Nan Zheng
School of Data Science and Artificial Intelligence
Dongbei University of Finance and Economics
Dalian, 116025
PR China

Abstract:

This paper establishes a new criterion for the total positivity of Riordan arrays with parameterized A- and Z-sequence generating functions. We demonstrate the effectiveness of this criterion by proving the total positivity of several Riordan array classes.

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(Concerned with sequences A007317 A007852 A100192 A101478 A104259 A113955 A202039.)

Received July 17 2025; revised versions received July 19 2025; December 5 2025; December 6 2025. Published in Journal of Integer Sequences, December 6 2025.

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