Hacène Belbachir
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View article: Enumeration of parallelogram polycubes
Enumeration of parallelogram polycubes Open
In this paper, we give the Dirichlet generating function of parallelogram polycubes according to the volume and the width in terms of multivariate zeta functions. We also enumerate them according to the width, the length and the depth. All…
View article: A study on tricomplex polynomials
A study on tricomplex polynomials Open
Tricomplex numbers are a generalization of bicomplex numbers. In this paper, we detail a technique for finding the roots of tricomplex polynomials. We generalized then the process to multicomplex polynomials. We first give an idempotent-re…
View article: On the Horadam sequence of order three
On the Horadam sequence of order three Open
In this paper, we define a generalized Horadam triangle in which the sum of elements located along the diagonal lines corresponds to the terms of generalized Horadam sequence of order three. We establish a relation between generalized Hora…
View article: The Towers of Fibonacci, Lucas, Pell, and Jacobsthal
The Towers of Fibonacci, Lucas, Pell, and Jacobsthal Open
We present in this paper four new variants of the Tower of Hanoi problem, the optimal solution of each of these variants is related to one of the four known numbers Fibonacci, Lucas, Pell, and Jacobsthal. We give an optimal solution to eac…
View article: An improved quantum-inspired particle swarm optimisation approach to reduce energy consumption in IoT networks
An improved quantum-inspired particle swarm optimisation approach to reduce energy consumption in IoT networks Open
The Internet of Things (IoT) plays a pivotal role in modern society, connecting everyday objects to the internet and enabling smart functionalities that enhance efficiency, convenience, and sustainability across multiple sectors. As IoT ne…
View article: Unified approach to Carlitz and Cigler q-analogue for the bi-periodic Fibonacci and Lucas sequences
Unified approach to Carlitz and Cigler q-analogue for the bi-periodic Fibonacci and Lucas sequences Open
Inthis study, our aim is to establish and generalize a q-analogue for the bi-periodic Fibonacci and Lucas polynomials. We introduce two types of q-analogue for the bi-periodic Lucas polynomials, namely the q-bi-periodic Lucas polynomials o…
View article: Bi-periodic Fibonomial coefficients
Bi-periodic Fibonomial coefficients Open
In the present study, we introduce a new generalization of Fibonomial coefficients known as bi-periodic Fibonomial coefficients, which can be expressed in relation to bi-periodic Fibonacci num-bers. We establish various properties of these…
View article: Deep learning-based Covid-19 diagnosis: a thorough assessment with a focus on generalization capabilities
Deep learning-based Covid-19 diagnosis: a thorough assessment with a focus on generalization capabilities Open
The Covid-19 pandemic has significantly spurred the development of deep learning (DL) models for the pathology automatic diagnosis based on CT scan images. However, the assumption about the generalization of the proposed models remains to …
View article: Hyper-Leonardo p-numbers and associated norms
Hyper-Leonardo p-numbers and associated norms Open
In this paper, we introduce hyper-Leonardo p-numbers, which generalize "hyper-Leonardo numbers".We establish their various combinatorial properties, including recurrence relations, summation formulas, and the generating function.We also co…
View article: Weighted binomial sums using characters of the symmetric group
Weighted binomial sums using characters of the symmetric group Open
Irreducible characters plays a crucial role in the representation theory of finite groups, namely the symmetric group Sn. In the current paper, we use the irreducible characters of Sn to define new weighted binomial coefficient sums. We us…
View article: Bi-Periodic Hyper-Fibonacci Numbers
Bi-Periodic Hyper-Fibonacci Numbers Open
In the present paper, we introduce and study a new generalization of hyper-Fibonacci numbers, called the bi-periodic hyper-Fibonacci numbers. Furthermore, we give a combinatorial interpretation using the weighted tilings approach and prove…
View article: Random approach to Tribonacci identity
Random approach to Tribonacci identity Open
This paper gives an expansion of the work of Benjamin, Arthur T., et al in ?random approached to Fibonacci identities? to a random approach to Tribonacci Identity.
View article: The Deranged Bell Numbers
The Deranged Bell Numbers Open
Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set [ n ] = {1, 2, … n }, this paper introduces the deranged partition as a free-fixed-block permutation of its blocks, th…
View article: On Recurrences in Generalized Arithmetic Triangle
On Recurrences in Generalized Arithmetic Triangle Open
In the present paper, we consider the generalized arithmetic triangle called GAT which is structurally identical to Pascal’s triangle for which we keep the Pascal’s rule of addition and we replace both legs by two sequences ( a n ) n ≥1 an…
View article: On the spectral norms of r-circulant and geometric circulant matrices with the bi-periodic hyper-Horadam sequence
On the spectral norms of r-circulant and geometric circulant matrices with the bi-periodic hyper-Horadam sequence Open
In this paper, we define the bi-periodic hyper-Horadam sequence {wn } n∈N and present its combinatorial properties.Moreover, we obtain upper and lower bounds for the spectral norms of different forms of the r -circulant and geometric circu…
View article: On $k$-generalized Lucas sequence with its triangle
On $k$-generalized Lucas sequence with its triangle Open
In this paper, we investigate several identities of $k$-generalized Lucas numbers with $k$-generalized Fibonacci numbers. We also establish a link between generalized $s$-Lucas triangle and bi$^{s}$nomial coefficients given by the coeffici…
View article: The (l,r)-Stirling numbers: A combinatorial approach
The (l,r)-Stirling numbers: A combinatorial approach Open
This work deals with a new generalization of r-Stirling numbers using l-tuple of permutations and partitions called (l,r)-Stirling numbers of both kinds. We study various properties of these numbers using combinatorial interpretations and …
View article: Continued fractions for bi-periodic Fibonacci sequence
Continued fractions for bi-periodic Fibonacci sequence Open
In this paper, we study generalized continued fractions for the expression of bi-periodic Fibonacci ratios.
View article: A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering
A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering Open
Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely nove…
View article: Enumerating moves in the optimal solution of the Tower of Hanoi
Enumerating moves in the optimal solution of the Tower of Hanoi Open
In the Tower of Hanoi problem, there is six types of moves between the three pegs. The main purpose of the present paper is to find out the number of each of these six elementary moves in the optimal sequence of moves. We present a recursi…
View article: The weighted Tower of Hanoi
The weighted Tower of Hanoi Open
The weighted Tower of Hanoi is a new generalization of the classical Tower of Hanoi problem, where a move of a disc between two pegs $i$ and $j$ is weighted by a positive real $w_{ij}\geq 0$. This new problem generalizes the concept of fin…
View article: Linear recurrence sequence associated to rays of negatively extended Pascal triangle
Linear recurrence sequence associated to rays of negatively extended Pascal triangle Open
We consider the extension of generalized arithmetic triangle to negative values of rows and we describe the recurrence relation associated to the sum of diagonal elements laying along finite rays. We also give the corresponding generating …
View article: Determinantal and permanental representations of companion sequences associated to the r-Fibonacci sequence
Determinantal and permanental representations of companion sequences associated to the r-Fibonacci sequence Open
Recently companion sequences of r-Fibonacci sequence were defined. The aim of this paper is to give some determinantal and permanental representations of these sequences via Hessenberg matrices. Several representations of classical sequenc…
View article: Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$
Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$ Open
In the present paper, for a positive integer $r$, we study bi-periodic $r$-Fibonacci sequence and its family of companion sequences, bi-periodic $r$-Lucas sequence of type $s$ with $1 \leq s \leq r$, which extend the classical Fibonacci an…
View article: On generalized Fibonacci and Lucas hybrid polynomials
On generalized Fibonacci and Lucas hybrid polynomials Open
In this paper, we introduce a new generalization of Fibonacci and Lucas hybrid polynomials. We investigate some basic properties of these polynomials such as recurrence relations, the generating functions, the Binet formulas, summation for…
View article: Asymmetric extension of Pascal-Delannoy triangles
Asymmetric extension of Pascal-Delannoy triangles Open
In this paper, we give a generalization of the Pascal triangle called the quasi s-Pascal triangle. For this, consider a set of lattice path, which is a dual approach to the definition of Ramirez and Sirvent: A Generalization of the k-bonac…
View article: Two-sided sampling plan for exponential distribution under type II censored samples
Two-sided sampling plan for exponential distribution under type II censored samples Open
Acceptance sampling plan paid the attention of many researchers in the last few years, their works focused basically on Bayesian sampling plans under one-sided decision function and different forms of censoring. In the present paper, a sin…
View article: DIAG a Diagnostic Web Application Based on Lung CT Scan Images and Deep Learning
DIAG a Diagnostic Web Application Based on Lung CT Scan Images and Deep Learning Open
Coronavirus disease is a pandemic that has infected millions of people around the world. Lung CT-scans are effective diagnostic tools, but radiologists can quickly become overwhelmed by the flow of infected patients. Therefore, automated i…
View article: Unified Bernoulli-Euler polynomials of Apostol type
Unified Bernoulli-Euler polynomials of Apostol type Open
The object of this paper is to introduce and study properties of unified Apostol-Bernoulli and Apostol-Euler polynomials noted by $\left\{\mathfrak{V_{n}}(x;λ;μ)\right\}_{n \geq 0}$. We study some arithmetic properties of $\left\{\mathfrak…