Higher member single coronoid

The focussing on formulas for single coronoids is continued in this chapter. It starts with a treatment of sequences of associated formulas for extremal single coronoids. This study leads to another subdivision of the extremal coronoids ground forms and higher members. The pertinent sections can be considered as a preparation to the enumeration of coronoid isomers, which is treated in the subsequent chapter. Also the process of building-up (Sect. 6.5) is highly relevant to the enumeration of isomers. 

For extremal single coronoids we shall define ground forms and higher members in connection with a sequence of formulas (uq Sq), (n . , (nj. in analogy with the... 

Definition 6.2 A higher member (of single coronoids) is synonymous with a drcumextremal single coronoid. 

Definition 6.4 . (a) A perfect higher member (of single coronoids) is defined by having the same formula as a Wold k > 1) circumscribed perfect ground form, (b) An imperfect higher member has the same formula as a A —fold circumscribed imperfect ground form. 

Let (TijjjP symboUze the formula for a Aj-fold circumscribed gP system. Then this formula (for k > 0) pertains to the perfect higher members of single coronoids. From (3) and (5.52) one obtains the general formulation ... 

Figure 3 shows a dot diagram for the formulas of single coronoids as in Fig. 5.8. However, more detailed information about the extremal (A) systems is included formulas for ground forms and higher members, both perfect and imperfect, are indicated.

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