Pauli–Leonardo quaternions

Zehra İşbilir, Mahmut Akyiğit and Murat Tosun
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 1, Pages 1–16
DOI: 10.7546/nntdm.2023.29.1.1-16
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Authors and affiliations

Zehra İşbilir
Department of Mathematics, Faculty of Art and Science,
Düzce University, Düzce, 81620, Turkey

Mahmut Akyiğit
Department of Mathematics, Faculty of Science,
Sakarya University, Sakarya, 54187, Turkey

Murat Tosun
Department of Mathematics, Faculty of Science,
Sakarya University, Sakarya, 54187, Turkey

Abstract

In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities, and the sum properties of these novel quaternions. In addition, we investigate the interrelations between Pauli–Leonardo quaternions and the Pauli–Fibonacci, Pauli–Lucas quaternions. Moreover, we create some algorithms that determine the terms of the Pauli–Leonardo quaternions. Finally, we generate the matrix representations of the Pauli–Leonardo quaternions and ℝ-linear transformations.

Keywords

  • Leonardo numbers
  • Pauli quaternions
  • Pauli–Leonardo quaternions

2020 Mathematics Subject Classification

  • 11K31
  • 11R52

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Manuscript history

  • Received: 28 July 2022
  • Revised: 28 November 2022
  • Accepted: 17 December 2022
  • Online First: 25 January 2023

Copyright information

Ⓒ 2023 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).

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Cite this paper

İşbilir, Z., Akyiğit, M., & Tosun, M. (2023). Pauli–Leonardo quaternions. Notes on Number Theory and Discrete Mathematics, 29(1), 1-16, DOI: 10.7546/nntdm.2023.29.1.1-16.

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