Enumeration: General Treatment and Coarse Classifications

Abstract

By enumeration of coronoid systems the counting of all possible non-isomor-phic systems within a class of coronoids is understood. Usually (but not always) the number of hexagons (h) is the leading parameter. The primitive coronoid with h=S (Fig. 2.1) is the smallest coronoid and unique with this number of hexagons. The numbers of non-isomorphic coronoid systems with h — 9, 10 and 11 are 5, 43 and 283, respectively. These numbers increase rapidly, roughly by a factor between 6 and 7 for every h unit, but yet they are known for several additional h values (see below, throughout this chapter). We are not only interested in the grand total of coronoid systems, but also in subdivisions into different classes. In this connection one speaks about classification. This aspect is especially important for large h values.