Abstract
Using the notion of fuzzy subset, the algebraic formulation of the constant of stereogenic pairing equilibria between skeletal analogs (previously disclosed) is connected to symmetry group theory. A distinction is introduced between geometrical (skeletal) symmetry and topographical (numerical parameters) symmetry. In order to describe “topographical symmetry”, a formal extended definition of a subgroup is proposed. Fuzzy subsets of the skeletal groupG are endowded with a structure which can be defined without referring to the geometrical representation of the abstract group isomorphic toG. The relevance of these propositions is evidenced by their “integer interpretation” meeting basic definitions of group theory, as well as by their role in expressing chemical pairing constants.
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Chauvin, R. Chemical algebra. I: Fuzzy subgroups. J Math Chem 16, 245–256 (1994). https://doi.org/10.1007/BF01169211
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DOI: https://doi.org/10.1007/BF01169211