Abstract
The correlation described over twenty years ago by Matula between the prime factorization of integers and the class of alkanes is re-examined with a view to explaining the probable reason why there have, to date, been no major extensions of this idea. By considering the class of alkanes as a one-dimensional one-parameter system, a new perspective on the method is gained that is amenable to extension, but in a different direction than originally anticipated. With this new perspective, the classes of polybenzenes and polymantanes are seen to be the representatives of two- and three-dimensional one-parameter systems, respectively. A “nomenclature”, comparable to one that Matula used for alkanes, is created that gives a unique canonical name to all possible combinations of either polybenzene or polymantane modules. Such a “nomenclature” contains a “built-in” means of positioning the molecule in the field of interest in accordance with arbitrary pre-selected criteria, such as Patterson's rules, and also coding that indicates symmetries inherent in the structure of this “molecule”.
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