Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 09 03 Homogeneous symmetric functions and new generating functions for products of some numbers with bivariate Mersenne and bivariate Mersenne Lucas polynomials 15012 10.22049/cco.2025.29817.2170 EN Amina Daoui Department of Mathematics,University Ferhat Abbas Setif1, Algeria Laboratory of Mathematics and their Interactions, Abd el Hafidh Boussof University center of Mila, Algeria Ali Boussayoud LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria Noureddine Midoune Department of mathematics, M’sila University, M’sila, Algeria Laboratory of Pure and Applied Mathematics, Algeria Khadidja Boubellouta LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria Journal Article 2024 06 08 The aim of this paper is to provide some operators for symmetric functions for the purpose of obtaining new generating functions for products of k-Fibonacci, $K$-Lucas and $k$-Jacobsthal numbers, $K$-Mersenne numbers bivariate complex Fibonacci poly nomials and Cheb yshev poly nomials with bivariate Mersenne and bivariate Mersenne Lucas polynomials . https://comb-opt.azaruniv.ac.ir/article_15012_3f91dd5f396a917dc63a44ae8cd98e0c.pdf