Recurrence Relations and Determinants
Combinatorics
2011-12-13 v1
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 -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 -determinants.
Cite
@article{arxiv.1112.2466,
title = {Recurrence Relations and Determinants},
author = {Milan Janjic},
journal= {arXiv preprint arXiv:1112.2466},
year = {2011}
}