Relationship of Bell’s Polynomial Matrix and k-Fibonacci Matrix

  • Mawaddaturrohmah Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia
  • Sri Gemawati Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia
Keywords: Bell’s Polynomial Number, Bell’s Polynomial Matrix, k-Fibonacci Number, k-Fibonacci Matrix

Abstract

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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Published
2020-02-27
Section
Articles