Relationship of Bell’s Polynomial Matrix and k-Fibonacci Matrix
AbstractThe Bell’s polynomial matrix is expressed as , where each of its entry represents the Bell’s polynomial number.This Bell’s polynomial number functions as an information code of the number of ways in which partitions of a set with certain elements are arranged into several non-empty section blocks. Furthermore, thek-Fibonacci matrix is expressed as , where each of its entry represents the k-Fibonacci number, whose first term is 0, the second term is 1 and the next term depends on a positive integer k. This article aims to find a matrix based on the multiplication of the Bell’s polynomial matrix and the k-Fibonacci matrix. Then from the relationship between the two matrices the matrix is obtained. The matrix is not commutative from the product of the two matrices, so we get matrix Thus, the matrix , so that the Bell’s polynomial matrix relationship can be expressed as
M. Abbas and S. Bouroubi, “On New Identities for Bell’s Polynomial”, Discrete Mathematics, vol. 293, pp. 5–10, March. 2005.
Comtet, “Advanced Combinatorics”, Reidel Publishing Company, Dordrecht and Boston, 1974.
S. Falcon, “The k-Fibonacci Matrix and The Pascal Matrix”, Central European Journal of Mathematics, vol. 9, pp. 1403-1410, August. 2011.
S. Falcon and A. Plaza, “k-Fibonacci Sequences Modulo m”, Chaos Solitons and Fractals, vol. 41, pp. 497-504, Feb. 2009.
K. K. Kataria and P. Vellaisamy, “Correlation Between Adomian and Partial Exponential Bell Polynomials”, Discrete Mathematics, vol 10, pp. 168–185, May 2016.
M. Mihoubi, “Bell Polinomiyals and Binomial Type Sequences”, Discrete Mathematics, vol 308, pp. 2450–2459, May 2007.
F. Qi, D. W. Niu, D. Lim, and B. N. Guo, “Some Properties and Application of Multivariate Exponential Polynomial“, Archives Ouvertes, vol. 8, pp. 1–22, Aug. 2018.
G. P. S. Rathore, A.A. Wani, and K. Sisodiya, “Matrix Representation of Generalized k-Fibonacci Sequence”, OSR Journal of Mathematics, vol, 12, pp. 67–72, Jan. 2016.
T. Wahyuni, S. Gemawati and Syamsudhuha, “On Some Identities of k-Fibonacci Sequences Modulo Ring "Z" _"6" dan"Z" _"10" “, Applied Mathematical Sciences, vol. 12, pp. 441–448, March. 2018.
W. Wang and T. Wang, “Identities via Bell matrix and Fibonacci matrix”, Discrete Applied Mathematics, vol. 156, pp. 2793–2803, Feb.2008.
W. Wang and T. Wang, “Matrices Related to the Bell Polynomials”, Linear Algebra and Its Applications, vol. 422, pp.139–154, Nov. 2007.
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