A Study on Dual Generalized Pierre Numbers
Year: 2025
Type: article
Abstract: In this study, we introduce a new family of number sequences, termed generalized dual Pierre numbers, defined over the bidimensional Clifford algebra of hyperbolic numbers. This algebraic framework enables the extension of classical integer sequences into a broader hypercomplex domain. As special cases, we examine the dual Pierre numbers and the dual Pierre Lucas numbers, thereby connecting our results with well-known recursive sequences. For these sequences, we derive closed-form Binet-type formulas, construct their generating functions, and establish several summation identities. Furthermore, we develop matrix representations associated with the proposed sequences, which not only provide elegant proofs of recurrence relations but also suggest potential applications in linear algebra and operator theory. Overall, this work enriches the theory of integer sequences by embedding them into the Clifford algebra framework, unveiling new structural connections, analytical techniques, and possible applications in both pure and applied mathematics.
Authors: Sercan DOGAN, Yuksel SOYKAN
Institution: Zonguldak Bülent Ecevit University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4417432341