Yazar "Civciv, Haci" seçeneğine göre listele

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    A generalization of tridiagonal matrix determinants, Fibonacci and Lucas numbers
    (PERGAMON-ELSEVIER SCIENCE LTD, 2009) Nalli, Ayse; Civciv, Haci
    In this paper, we construct the symmetric tridiagonal family of matrices M(-alpha-beta)(k), k = 1, 2,... whose determinants form any linear subsequence of the Fibonacci numbers. Furthermore, we construct the symmetric tridiagonal family of matrices T(-alpha-beta)(k), k = 1, 2,... whose determinants form any linear subsequence of the Lucas numbers. Thus we give a generalization of the presented in Cahill and Narayan (2004) [Cahill ND, Narayan DA. Fibonacci and Lucas numbers as tridiagonal matrix determinants. Fibonacci Quart 2004;42(3):216-21]. (C) 2007 Elsevier Ltd. All rights reserved.
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    Notes on the (s, t)-Lucas and Lucas Matrix Sequences
    (CHARLES BABBAGE RES CTR, 2008) Civciv, Haci; Turkmen, Ramazan
    In this article, defining the matrix extensions of the Fibonacci and Lucas numbers we start a new approach to derive formulas for some integer numbers which have appeared, often surprisingly, as answers to intricate problems, in conventional and in recreational Mathematics. Our approach provides a new way of looking at integer sequences from the perspective of matrix algebra, showing how several of these integer sequences relate to each other.
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    On the (s,t)-fibonacci and fibonacci matrix sequences
    (CHARLES BABBAGE RES CTR, 2008) Civciv, Haci; Turkmen, Ramazan
    It is always fascinating to see what results when seemingly different areas mathematics overlap. This article reveals one such result; number theory and linear algebra are intertwined to yield complex factorizations of the classic Fibonacci, Pell, Jacobsthal, and Mersenne numbers. Also, in this paper we define a new matrix generalization of the Fibonacci numbers, and using essentially a matrix approach we show some properties of this matrix sequence.