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arXiv · 1112.2466

Recurrence Relations and Determinants

Milan Janjic
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Abstract

We examine relationships between two minors of order n of some matrices of n rows and n+r columns. This is done through a class of determinants, here called $n$-determinants, the investigation of which is our objective. We prove that 1-determinants are the upper Hessenberg determinants. In particular, we state several 1-determinants each of which equals a Fibonacci number. We also derive relationships among terms of sequences defined by the same recurrence equation independently of the initial conditions. A result generalizing the formula for the product of two determinants is obtained. Finally, we prove that the Schur functions may be expressed as $n$-determinants.

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Milan Janjic. 2011-12-12. Recurrence Relations and Determinants. https://arxiv.org/abs/1112.2466

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