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We prove a constant term theorem which is useful for finding weightpolynomials for Ballot/Motzkin paths in a strip with a fixed number ofarbitrary `decorated' weights as well as an arbitrary `background' weight. OurCT theorem, like Viennot's lattice path theorem from which it is derivedprimarily by a change of variable lemma, is expressed in terms of orthogonalpolynomials which in our applications of interest often turn out to benon-classical. Hence we also present an efficient method for finding explicitclosed form polynomial expressions for these non-classical orthogonalpolynomials. Our method for finding the closed form polynomial expressionsrelies on simple combinatorial manipulations of Viennot's diagrammaticrepresentation for orthogonal polynomials. In the course of the paper we alsoprovide a new proof of Viennot's original orthogonal polynomial lattice paththeorem. The new proof is of interest because it uses diagonalization of thetransfer matrix, but gets around difficulties that have arisen in past attemptsto use this approach. In particular we show how to sum over a set of implicitlydefined zeros of a given orthogonal polynomial, either by using properties ofresidues or by using partial fractions. We conclude by applying the method totwo lattice path problems important in the study of polymer physics as modelsof steric stabilization and sensitized flocculation.

Chebyshev type lattice path weight polynomials by a constant term method