TY - JOUR ID - 4581 TI - $d-$Fibonacci and $d-$Lucas polynomials JO - Journal of Mathematical Modeling JA - JMM LA - en SN - 2345-394X AU - Sadaoui, Boualem AU - Krelifa, Ali AD - LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana, 44225 Algeria AD - LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana 44225, Algeria Y1 - 2021 PY - 2021 VL - 9 IS - 3 SP - 425 EP - 436 KW - $d-$Fibonacci polynomials KW - $d-$Lucas polynomials KW - Riordan arrays KW - Pascal matrix KW - $Q_{d}-$Fibonacci matrix DO - 10.22124/jmm.2021.17837.1538 N2 - Riordan arrays give us an intuitive method of solving combinatorial problems. They also help to apprehend number patterns and to prove many theorems. In this paper, we consider the Pascal matrix, define a new generalization of Fibonacci and Lucas polynomials called $d-$Fibonacci and $d-$Lucas polynomials (respectively) and  provide their properties. Combinatorial identities are obtained for the defined polynomials and by using Riordan method we get factorizations of Pascal matrix involving $d-$Fibonacci polynomials. UR - https://jmm.guilan.ac.ir/article_4581.html L1 - https://jmm.guilan.ac.ir/article_4581_d5a4d10c1688c9b12ffff9830972967e.pdf ER -