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- Hacène Belbachir, Farid Bencherif
- Ars Comb.
- 2011

This paper is devoted to the study of certain unimodal sequences related to binomial coefficients. Although the paramount purpose is to prove unimodality, in a few cases we even determine the maxima of the sequences. Our new results generalize some earlier theorems on unimodality. The proof techniques are quite varied. This research is supported by the… (More)

In this paper we generalize to bivariate Fibonacci and Lucas polynomials, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate bases are families of integers satisfying remarkable recurrence relations.

In this paper, we establish a formula expressing explicitly the general term of a linear recurrent sequence, allowing us to generalize the original result of J. McLaughlin [7] concerning powers of a matrix of size 2, to the case of a square matrix of size m ≥ 2. Identities concerning Fibonacci and Stirling numbers and various combinatorial relations are… (More)

- Hacène Belbachir, Farid Bencherif
- Ars Comb.
- 2013

In this paper, we establish several formulae for sums and alternating sums of products of generalized Fibonacci and Lucas numbers. In particular, we recover and extend all results of Z. Čerin [2, 2005] and Z. Čerin and G. M. Gianella [3, 2006], more easily.

- Farid Bencherif, Leila Hayet Mouss, Mohammed Meguellati
- 2013 5th International Conference on Modeling…
- 2013

Quality Function Deployment (QFD) is an effective tool to enhance customer satisfaction, develop the product quality and enhance competitive advantages in the market. In developing new products and projects, we receive the needs from the customer, pass it around a corporate communication circle, and eventually return it to the customer in the form of the… (More)

In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations.

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