Abstract
Abstract Polygonal systems correspond to polycyclic hydrocarbons. The numbers of C n H s isomers for these systems are studied systematically. Complete mathematical solutions are reported for systems with the numbers of polygons (or rings), r , up to five, and arbitrary polygon (ring) sizes q ⪖ 3. Explicit combinatorial formulae are given for all cases (nine subclasses) with r ⪕ 4. For r ⪕ 5 (23 subclasses) the solutions are presented in terms of generating functions. The number of degrees of freedom, ϕ, depends on the number of independently varying polygon sizes and sites of annelation. This parameter (ϕ), together with the symmetry properties, are used as a novel basis of classification of the polygonal systems.
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