Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial enumeration of groups, graphs, and chemical compounds
Graph Theory, 1736-1936
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The theory of chemical enumeration can be considered to have reached maturity with the works by Balaban, and more specifically for the enumeration of alkane isomers, with the work of Polya and Read, the key points of which rely on the theory of generating function in relation with symmetry properties. The present paper, after briefly recalling the history and the basis of these theories, aims at indicating a new direction of research, which covers a new field of applications beyond the classical results of chemical enumeration, making use of the recent developments of computer algebra. This new direction aims at providing the fundamentals in order to generate explicitly 3D configurations of the stereo-isomers of alkane molecules and consider only some subclasses of the whole set of alkanes which are encountered in most applications. This capability associated with the obtained degree of symmetry of the generated stereo-isomers is of primary importance for applications in thermochemistry and chemical kinetics.