Perfect staircase

Furthermore, one should observe the termination of each row in the right-hand direction. This termination results in the staircase boundary. It is determined by the formulas situated at the extreme—right of each row, namely the formulas which pertain to the extremal polyhexes, as should be dear from the definition of these systems (Par. 3.3.4). When perfect extremal p-tuple coronoids are involved, then the corresponding staircase boundary reflects a part of the staircase boundary for benzenoids. It is specifically the part which corresponds to the benzenoids associated with the tuple coronoids in question. Thus, for instance, the staircase boundary for single coronoids has the same shape as the one for benzenoids when starting from C32H14 ovalene (cf. Table 5, where the start of this staircase boundary for benzenoids is indicated by thin lines). A staircase boundary of this kind, determined by perfect extremal coronoids or extremal benzenoids, shall be referred to as a perfect staircase (boundary). If imperfect extremal coronoids are involved we shall call it an imperfect staircase. 

In Table 3 "everything is perfect". The formulas at the extreme right of each row pertain to perfect extremal single coronoids, and therefore the right-hand boundary is a perfect staircase cf. Par. 3.7.3. 

At Tonic, the generation named Britney walked up and down the steel staircases, balancing their martini glasses with perfect form, gripping them gingerly at the rim. 

Figure 20. Total integral level density N E) as obtained for Model IVa. The mapping calculation (y = 1, upper line) is seen to match the quantum staircase function almost perfectly, while the mean-field trajectory results (y = 0, lower line) underestimate the correct level density considerably.

In the above diagrams the staircase boundaries are indicated by heavy lines. For the portions where they are imperfect they are augmented by stippled lines to the shapes which conform with perfect boundaries. Hence it should be understood that the parenthesized formulas actually do not exist for the coronoids in question. The heavy formulas pertain to perfect extremal coronoids. 

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