Bivariate Leonardo polynomials and Riordan arrays

Yasemin Alp and E. Gökçen Koçer
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 2, Pages 236–250
DOI: 10.7546/nntdm.2025.31.2.236-250
Full paper (PDF, 234 Kb)

Details

Authors and affiliations

Yasemin Alp
Department of Education of Mathematics and Science, Faculty of Education, Selcuk University
Konya, Türkiye

E. Gökçen Koçer
Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University
Konya, Türkiye

Abstract

In this paper, bivariate Leonardo polynomials are defined, which are closely related to bivariate Fibonacci polynomials. Bivariate Leonardo polynomials are generalizations of the Leonardo polynomials and Leonardo numbers. Some properties and identities (Cassini, Catalan, Honsberger, d’Ocagne) for the bivariate Leonardo polynomials are obtained. Then, the Riordan arrays are defined by using bivariate Leonardo polynomials.

Keywords

• Binet’s formula
• Fibonacci polynomials
• Leonardo numbers
• Riordan arrays

2020 Mathematics Subject Classification

• 11B37
• 11B39
• 11B83
• 05A15
• 15A09

References

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Manuscript history

• Received: 2 October 2024
• Revised: 6 May 2025
• Accepted: 7 May 2025
• Online First: 7 May 2025

Copyright information

Ⓒ 2025 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).