As a generalization of earlier work of the author J. Chem. Phys.40,2248 (1964);45,1080 (1966) a completely noncombinatorial method is derived which gives for any state the exact thermodynamic properties of a system of particles on a lattice infinite in one dimension. The method appears to be essentially equivalent to, but somewhat simpler in development and application than, the matrix method used for the same problems recently. Interaction of unit configurations is explicitly considered only at lattice boundaries, leading directly to a set of independent algebraic equations giving the complete solution for a specified state. Two simple examples are given to which alternative combinatorial procedures can be readily applied without approximations, yielding identical explicit results. The general method first given is modified for the imposition of artificial density constraints, and as an illustration it is shown how this variation improves markedly, over the range of disordered densities, the convergence to an infinite plane of the hardhyphen;core squarehyphen;lattice fluid with nearesthyphen;neighbor exclusion.
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