Volume 31 ▶ Number 1 ▷ Number 2
- Volume opened: 1 May 2025
- Status: In progress
A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers
Original research paper. Pages 201–210
Nazmiye Yılmaz, Esra Kırmızı Çetinalp and Ömür Deveci
Full paper (PDF, 232 Kb) | Abstract
In this research, several types of definitions of the quaternion-type cyclic-balancing sequence are presented. The Cassini formula and generating function of these sequences are also obtained for all types. The quaternion-type cyclic-balancing sequences modulo 
the first step to transferring this topic to group theory, are examined. These sequences in finite groups are then defined. Eventually, the lengths of periods for these sequences of the generalized quaternion group are calculated.
the first step to transferring this topic to group theory, are examined. These sequences in finite groups are then defined. Eventually, the lengths of periods for these sequences of the generalized quaternion group are calculated.
A new approach to tridiagonal matrices related to the Sylvester–Kac matrix
Original research paper. Pages 211–227
Efruz Özlem Mersin and Mustafa Bahşi
Full paper (PDF, 307 Kb) | Abstract
The Sylvester–Kac matrix, a well-known tridiagonal matrix, has been extensively studied for over a century, with various generalizations explored in the literature. This paper introduces a new type of tridiagonal matrix, where the matrix entries are defined by an integer sequence, setting it apart from the classical Sylvester–Kac matrix. The aim of this paper is to investigate several fundamental properties of this generalized matrix, including its algebraic structure, determinant, inverse, LU decomposition, characteristic polynomial, and various norms.
This volume of the International Journal “Notes on Number Theory and Discrete Mathematics” is published with the financial support of the Bulgarian National Science Fund, Grant Ref. No. KP-06-NP6/12/02.12.2024.
