Relationship of Bell’s Polynomial Matrix and k-Fibonacci Matrix
Keywords:
Bell’s Polynomial Number, Bell’s Polynomial Matrix, k-Fibonacci Number, k-Fibonacci MatrixAbstract
The 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
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