quelques théorémes sur les fonctions symétriques et leurs applications

Abstract

This dissertation is devoted to the study of some fundamental theorems on symmetric functions and their applications. After presenting the necessary preliminary notions, we investigate elementary and complete symmetric functions together with several algebraic relations connecting them. We then use generating nctions as a principal tool to establish various results concerning symmetric functions and their applications to certain recurrent sequences and families of polynomials. In particular, we derive generating functions associated with Pell–Lucas numbers, bivariate Lucas polynomials, and bivariate Jacobsthal– Lucas polynomials. The obtained results highlight the importance of symmetric functions in the combinatorial and algebraic study of sequences and polynomials