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Research Article

Enumeration of Unbranched Catacondensed Polygonal Systems: General Solution for Two Kinds of Polygons

S. J. Cyvin,* J. Brunvoll, and B. N. Cyvin

Department of Physical Chemistry, The University of Trondheim, N-7034 Trondheim-NTH, Norway

J. Chem. Inf. Comput. Sci., 1997, 37 (3), pp 460–466

DOI: 10.1021/ci960012x

Publication Date (Web): May 27, 1997

In papers with more than one author, the asterisk indicates the name of the author to whom inquiries about the paper should be addressed.

Abstract

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.