M. BENOUMHANI Moussa

MCA

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Department

Mathematics Department

Research Interests

Discrete Mathematics and Elementary Number Theory

Contact Info

University of M'Sila, Algeria

Email : moussa.benoumhani@univ-msila.dz

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Recent Publications

2019

Chains in lattices of mappings and finite fuzzy topological spaces

In this paper, we establish several results concerning chains in
Y
X
, the lattice of mappings from a finite set X into a finite totally ordered set Y. We compute the total number and the cardinalities of several collections of chains. As a byproduct we determine the total number of chained Y-fuzzy topologies defined on X. Several related and other well known results are obtained as corollaries. Also some natural questions are presented for further investigations
Citation

M. BENOUMHANI Moussa, (2019), "Chains in lattices of mappings and finite fuzzy topological spaces", [national] Journal of Combinatorial Theory, Series A , Elsevier

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2017

Finite fuzzy topological spaces. ‏

We compute for the first time, the number of fuzzy topologies defined on a finite set and having a small number of open sets. Certain cases, where the number of open sets is large, are also considered. Several well known results are obtained as corollaries. The paper is ended by some questions for future investigations.
Citation

M. BENOUMHANI Moussa, Ali Jaballah, , (2017), "Finite fuzzy topological spaces. ‏", [national] Fuzzy Sets and Systems , Elsevier

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2012

On the Modes of the Independence Polynomial of the Centipede.

The independence polynomial of the graph called the centipede has only real zeros. It follows that this polynomial is log-concave, and hence unimodal. Levit and Man- drescu gave a conjecture about the mode of this polynomial. In this paper, the exact value of the mode is determined, and some central limit theorems for the sequence of the coefficients are established.
Citation

M. BENOUMHANI Moussa, (2012), "On the Modes of the Independence Polynomial of the Centipede.", [national] Journal of Integer Sequences , University of waterloo

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2010

Finite topologies and partitions.

Let E be a set with n elements, and let T(n,k) be the number of all labeled topologies having k open sets that can be defined on E. In this paper, we compute these numbers for k ≤ 17, and arbitrary n, as well as tN0(n,k), the number of all unlabeled non-T0 topologies on E with k open sets, for 3 ≤ k ≤ 8.
Citation

M. BENOUMHANI Moussa, Messoud Kolli, , (2010), "Finite topologies and partitions.", [national] Journal of Integer Sequences , University of waterloo

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2006

The number of topologies on a finite set.

Let X be a finite set having n elements. How many different labeled topologies one can define on X? Let T(n,k) be the number of topologies having k open sets. We compute T(n,k) for 2 ≤ k ≤ 12, as well as other results concerning T0 topologies on X havingn+4≤k≤n+6opensets.
Citation

M. BENOUMHANI Moussa, (2006), "The number of topologies on a finite set.", [national] Journal of Integer sequences , university of waterloo

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2003

A sequence of binomial coefficients related to Lucas and Fibonacci numbers.

Let L(n, k) = n n−k . We prove that all the zeros of the polynomial Ln(x) = n−k k
L(n, k)xk are real. The sequence L(n, k) is thus strictly log-concave, and hence unimodal k≥0
with at most two consecutive maxima. We determine those integers where the maximum is reached. In the last section we prove that L(n, k) satisfies a central limit theorem as well as a local limit theorem.
Citation

M. BENOUMHANI Moussa, (2003), "A sequence of binomial coefficients related to Lucas and Fibonacci numbers.", [national] Journal of integer sequences , University of waterloo

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1999

Log-concavity of Whitney numbers of Dowling lattices.

We prove that the generating polynomial of Whitney numbers of the second kind of Dowling lattices has only real zeros.
Citation

M. BENOUMHANI Moussa, (1999), "Log-concavity of Whitney numbers of Dowling lattices.", [national] Advances in Applied Mathematics , academic press

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1997

"On some numbers related to Whitney numbers of Dowling lattices."

We study some polynomials arising from Whitney numbers of the second kind of Dowling lattices. Special cases of our results include well-known identities involving Stirling numbers of the second kind. The main technique used is essentially due to Rota.
Citation

M. BENOUMHANI Moussa, (1997), ""On some numbers related to Whitney numbers of Dowling lattices."", [national] Advances in Applied Mathematics , elsevier

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1996

Sur une proprieté des polynômes a racines réelles négatives

Interprétation probabiliste Polynôme Racine négative Racine polynôme Racine réelle
Citation

M. BENOUMHANI Moussa, (1996), "Sur une proprieté des polynômes a racines réelles négatives", [national] Journal de Mathématiques Pures et Appliqués 1(75):85-105 , Elsevier

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On Whitney numbers of Dowling lattices

We give some generating functions, recurrence relations for Whitney numbers of Dowling lattices, an explicit formula for Whitney numbers of the second kind, and other relations.
Citation

M. BENOUMHANI Moussa, (1996), "On Whitney numbers of Dowling lattices", [national] Disctrete mathematics , ELSEVIER

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