Matrix factorization of the n × n shift Bell matrix

Add time:07/30/2019    Source:sciencedirect.com

Let Bn=[Bn,k]n,k⩾0 be the Bell matrix. Define the n×n shift Bell matrix Pn,k by (Pn,k)i,j=Bk+i−1,k+j−1 for i,j=1,2,⋯n and k=0,1,2⋯. In this paper, matrix factorizations of the n×n shift Bell matrix and the n×n generalized Riordan matrix are studied. As a result, many lower triangular matrices related to Bell polynomials can be factorized by the corresponding matrices and some identities are derived from the matrix representations. In addition, some harmonic number identities are obtained from the Riordan array method.

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