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arXiv · 0901.2597

Generalized Pascal Triangles and Toeplitz Matrices

A. R. Moghaddamfar·S. M. H. Pooya
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Abstract

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see [1]). We present a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Toeplitz matrix and a unipotent upper triangular matrix. The determinant of a generalized Pascal matrix equals thus the determinant of a Toeplitz matrix. This equality allows us to evaluate a few determinants of generalized Pascal matrices associated to certain sequences. In particular, we obtain families of quasi-Pascal matrices whose principal minors generate any arbitrary linear subsequences F(nr+s) or L(nr+s), (n=1, 2, 3, ...) of Fibonacci or Lucas sequence.

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A. R. Moghaddamfar, S. M. H. Pooya. 2009-01-19. Generalized Pascal Triangles and Toeplitz Matrices. https://arxiv.org/abs/0901.2597

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