Generalization of Fibonomial Coefficients

Source: arXiv

ABSTRACT Following Lucas and then other Fibonacci people Kwasniewski had introduced and had started ten years ago the open investigation of the overall F-nomial coefficients which encompass among others Binomial, Gaussian and Fibonomial coefficients with a new unified combinatorial interpretation expressed in terms of cobweb posets' partitions and tilings of discrete hyperboxes. In this paper, we deal with special subfamily of T-nomial coefficients. The main aim of this note is to develop the theory of T-nomial coefficients with the help of generating functions. The binomial-like theorem for T-nomials is delivered here and some consequences of it are drawn. A new combinatorial interpretation of T-nomial coefficients is provided and compared with the Konvalina way of objects' selections from weighted boxes. A brief summary of already known properties of T-nomial coefficients is served. Comment: 13 pages, The Internet Gian-Carlo Rota Polish Seminar article, No 9, Subject 5,

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    ABSTRACT: In this paper, we get new factorizations of Pascal matrix via Fibonomial coefficients named Fibo-Pascal matrix involving the k-Fibonacci matrix and k-Pell matrix. We give illustrative examples about these factorizations. If we get k=2, the well-known Fibonacci and Pell matrices are obtained and the factorizations in Tuglu and Kocer (The generalized Pascal matrices via Fibonomial coefficients, 2011) are the special cases of our factorizations. Keywords k-Fibonacci– k-Pell–Factorization–Fibonomial
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