A multidimensional extension of the combinatorics function technique. II. Linear and inhomogeneous partial difference equations

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Abstract
Recently the solution of multidimensional, linear, and homogeneous recurrence relations, or partial difference equations (PDE), was obtained via a multidimensional extension of the combinatorics function technique, developed by Antippa and Phares. Combinatorics functions of the first and second kind are representations of ’’restricted’’ paths connecting two points in an n-dimensional space. These functions are shown to give the solution of the most general linear and inhomogeneous PDE. The consistency of the PDE with the initial value conditions is also discussed. Applications of the method are given elsewhere.