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A straightforward model for deposition and evaporation on discrete cells of afinite array of any dimension leads to a matrix equation involving aSylvester-Kac type matrix. The eigenvalues and eigenvectors of the generalmatrix are determined for an arbitrary number of cells. A variety of models towhich this solution may be applied are discussed.

The eigenpairs of a Sylvester-Kac type matrix associated with a simple model for one-dimensional deposition and evaporation