Discrete path approach to linear recursion relations

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Abstract
It is shown that the solutions of linear homogeneous recursion relations, with arbitrarily specified boundary conditions, are related, by a mapping, to the totality of discrete paths joining the two ends of an interval and made up of a predetermined set of directed segments. We study the dependence of these solutions on the way the boundary conditions are specified. When the boundary conditions are given as initial conditions, the present approach reduces to the formalism already developed for that specific case, and which is based on the partitions of an interval into classes.

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