11 citations · 45 across the 27 of their papers we have counts for
20 papers · 1 filter
Bounded compositions and products of chains, or bi(s)nomials everywhere from de Moivre's formula to spin multiplicities and constant-sum codes
Hacène Belbachir, José Ricardo G. Mendonça
How many ways are there to select objects from types when type is available in only copies? For equal bounds, this is de Moivre's problem of obtaining a prescri…
Circular s-choice parking functions: an exact closed formula via rotational symmetry
Hacène Belbachir, Asma Recioui, Abdelhakim Ait-Zai
We study a circular variant of the -choice parking model: cars park on spots arranged on a circle, each car carrying an anchor and clockwise increments at leas…
Rotating-Memory Fibonacci Numbers and Periodic Tilings
Walid Abdelaidoum, El-Mehdi Mehiri, Hacène Belbachir
We introduce and study the rotating-memory Fibonacci numbers, a periodic variable-order analogue of the Fibonacci sequence in which the number of preceding terms used in the recurr…
Generalized Steinhaus triangles generated by canonical basis vectors: periodicity and weight formulas
Randa Ouchene, Hacène Belbachir
A generalized Steinhaus -triangle is obtained from a binary sequence by repeatedly replacing each block of consecutive entries by its sum modulo . We study the triangles…
Delannoy--Steinhaus triangles over : weight spectrum, balanced triangles, and extremal values
Hacène Belbachir, Randa Ouchene
A Delannoy--Steinhaus triangle is obtained from a finite sequence by a recurrence governed by the Delannoy numbers. We introduce this construction over and…
A random approach to the multibonacci sequence
Hacène Belbachir, Hamza Zeggada
This paper presents a random approach to the multibonacci sequence. We generalise the model introduced by Benjamin, Levin, Mahlburg, and Quinn, which is based on a random tiling me…
The Towers of Fibonacci, Lucas, Pell, and Jacobsthal
El-Mehdi Mehiri, Saad Mneimneh, Hacène Belbachir
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, Luca…
Enumerating moves in the optimal solution of the Tower of Hanoi
Hacène Belbachir, El-Mehdi Mehiri
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 m…
Unified Bernoulli-Euler polynomials of Apostol type
Hacène Belbachir, Yahia Djemmada, Slimane Hadj-Brahim
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}…
The -Stirling numbers: a combinatorial approach
Hacène Belbachir, Yahia Djemmada
This work deals with a new generalization of -Stirling numbers using -tuple of permutations and partitions called -Stirling numbers of both kinds. We study various pro…
A Strehl Version of Fourth Franel Sequence
Hacene Belbachir, Yassine Otmani
We give a combinatorial identity related to the Franel numbers involving the sum of fourth power of binomial coefficients. Furthermore, investigating in J. Mikic's proof of the fir…
Asymmetric extension of Pascal-Dellanoy triangles
Said Amrouche, Hacène Belbachir
We give a generalization of the Pascal triangle called the quasi s-Pascal triangle where the sum of the elements crossing the diagonal rays produce the s-bonacci sequence. For this…
Directed Plateau Polyhypercubes
Abderrahim Arabi, Hacène Belbachir, Jean-Philippe Dubernard
In this paper, we study a particular family of polyhypercubes in dimension , the directed plateau polyhypercubes, according to to the width and a new parameter the lateral…
On central Fubini-like numbers and polynomials
Hacène Belbachir, Yahia Djemmada
We introduce the central Fubini-like numbers and polynomials using Rota approach. Several identities and properties are established as generating functions, recurrences, explicit f…
Plateau Polycubes and Lateral Area
Abderrahim Arabi, Hacène Belbachir, Jean-Philippe Dubernard
In this paper, we enumerate two families of polycubes, the directed plateau polycubes and the plateau polycubes, with respect to the width and a new parameter, the Lateral Area. We…
On the self-convolution of generalized Fibonacci numbers
Hacène Belbachir, Toufik Djellal, Jean-Gabriel Luque
We focus on a family of equalities pioneered by Zhang and generalized by Zao and Wang and hence by Mansour which involves self convolution of generalized Fibonacci numbers. We show…
Combinatorial approach of certain generalized Stirling numbers
Hacène Belbachir, Amine Belkhir, Imad Eddine Bousbaa
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expres…
Associated Lah numbers and r-Stirling numbers
Hacene Belbachir, Imad Eddine Bousbaa
We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stir…
Hankel hyperdeterminants, rectangular Jack polynomials and even powers of the Vandermonde
Hacene Belbachir, Adrien Boussicault, Jean-Gabriel Luque
We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of J…
Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution
Hacene Belbachir, Sadek Bouroubi, Abdelkader Khelladi
Using an explicit computable expression of ordinary multinomials, we establish three remarkable connections, with the q-generalized Fibonacci sequence, the exponential partial Bell…