Enumeration of Kekule Structures In One-dimensional Polymers"

One-dimensional polymer refers here to a polymer with a variable size in only one dimension. A new method for enumeration of Kekulć structures in such polymeric conjugated hydrocarbons is presented. It is quite general, but still efficient and simple to use. It is especially usefu1 for evaluation of the Kekule structure count, K, in polymers with regular structure, i. e. in those built up of equal monomers with uniform Iinking. In this case the method gives a recurrence relation and an explicit formula which enable the calculation of Kfor any number of monomers constituting the given polymer. Systems with more or less complex regularity, as well as those with some defect in structure, may also be successfully treated. The possibi'lities of application are demonstrated on several examples, and some specific details, e. g. the lowest order of recursion, are discussed.