Enumeration of Unbranched Catacondensed Polygonal Systems: General Solution for Two Kinds of Polygons
Sven Josef Cyvin, J. Brünvoll, Bjørg N. Cyvin · Journal of Chemical Information and Computer Sciences · 1997
An α- p -catapoly- q -gon is a catacondensed polygonal system with α p -gons and r − α q -gons, which represents a polycyclic conjugated hydrocarbon. Here r is the total number of polygons or rings. A complete mathematical solution for the numbers of nonisomorphic unbranched α- p -catapoly- q -gons is reported. It is expressed by complicated explicit formulas in r, α, p, and q, and it represents a generalization of several special cases studied previously. The solution was achieved by means of certain generalized triangular matrices with interesting mathematical properties.