What question did this study set out to answer?

To explore higher-order multiplicative Alqazzaz sequences and their behavior in hypercomplex algebra frameworks.

April 23, 20260 citationsOpen Access

Higher-Order Multiplicative Alqazzaz Sequences over Finite Root Sets and Hypercomplex Algebra

Key Points

To explore higher-order multiplicative Alqazzaz sequences and their behavior in hypercomplex algebra frameworks.
Introduced higher-order sequences over finite sets of roots of unity.
Extended sequence construction to third, fourth, and fifth orders.
Examined geometric implications through fractal generation in the complex plane.
Demonstrated diverse algebraic and dynamical structures from the proposed model.
Highlighted the impact of non-commutativity and non-associativity on sequence behavior.
Presented explicit examples to illustrate findings.

Abstract

In this paper, we introduce and study higher-order multiplicative Hn-Alqazzazsequences over finite sets of roots of unity. While the second-order case is generated from two preceding terms, we extend the construction to third-, fourth-,and fifth-order recurrences. We then generalize the framework to hypercomplexalgebras, including quaternions, octonions, and sedenions, in order to investigate the effect of non-commutativity and non-associativity on the behavior ofthe resulting sequences. In addition, we explore the geometric consequencesof these sequences through fractal generation in the complex plane. Severalexplicit examples are presented to illustrate the diversity of the algebraic anddynamical structures produced by the proposed model. These results suggestthat Alqazzaz sequences provide a flexible framework for studying multiplicativerecurrences across different algebraic settings

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