Generating Functions of Convolution Matrices

Yongzhi Yang

A chapter in Applications of Fibonacci Numbers, 2004, pp 289-295 from Springer

Abstract: Abstract Hoggatt and Bergum [2] studied the general expression for the entry in the i th row and the j th column of a convolution matrix and obtained row generating functions for the convolution matrix of the sequence {1, u 2, u 3, u 4, ...}. In this paper, we extend the Strong Convolution Decomposition Theorem [3] to a more general case. Based on this extension, we decompose a convolution matrix into a product of a lower trianglular matrix and the upper triangular Pascallike matrix. This interesting decomposition of a convolution matrix leads a novel approach to the subject proposed in [2] . Using this new method, we obtain a simple explicit formula for entries of a convolution matrix and row generating functions of the convolution matrix of the sequences {v n } and {u n }. Moreover, the approach developed here can be easily extended to a rather broad category of integer matrices.

Keywords: 15A23; 11B25; 11B65 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-306-48517-6_27

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DOI: 10.1007/978-0-306-48517-6_27

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