Perforated rectangle

Consider a perforated oblate rectangle as depicted in Fig. 9. Like a rectangle it is a system with two parameters (m, n). A perforated rectangle, Q(m, ), belongs to the multiple coronoids it has m — 1 corona holes. 

A study of the Kekule structure counts for perforated rectangles gave the result ... 

The designation "perforated rectangles" for certain single and multiple coronoids, of which the Kekul6 structures have been studied (Cyvin SJ, Cyvin and BrunvoU 1989a Chen and Cyvin 1989 Cyvin SJ, Cyvin, BrunvoU and Chen 1989 Chen, Cyvin et al. 1990), is compatible with the above definition of perforated benzenoids. 

Chen RS, Cyvin SJ (1989) Enumeration of Kekul Structures - Perforated Rectangles. J Mol Struct (Theochem) 200 251... 

Cyvin SJ, Cyvin BN, Brunvoll J, Chen RS (1989) The Number of Kekule Structures for Rectangle-Shaped Benzenoids, Part VIII - Some Perforated Rectangles. Monatsh Chem 120 833... 

The enumeration of Kekule structures for rectangle-shaped benzenoids is treated. Combinatorial formulas for K (the Kekule structure count) are derived by several methods. The oblate rectangles, Rj(m, n), with fixed values of m are treated most extensively and used to exemplify different procedures based on the method of fragmentation (chopping, summation), a fully computerized method (fitting of polynominal coefficients), application of the John-Sachs theorem, and the transfer-matrix method. For Rj(m, n) with fixed values of n the relevant recurrence relations are accounted for, and general explicit combinatorial K formulas are reported. Finally a class of multiple coronoids, the perforated oblate rectangles, is considered in order to exemplify a perfectly explicit combinatorial K formula, an expression for arbitraty values of the parameters m and n. 

Fig. 1. Left, the rat hippocampal region as seen in a horizontal section stained for AChE (c/. Fig. 2). The rectangle circumscribes a segment in the anterior part of regio superior. This rectangle is shown diagramatically in the 3 drawings on the right to illustrate A, the distribution of cell bodies B, AChE, and C, the types of neurones and synapses. An analogous situation exists for the area dentata. FH, fissura hippocampi B, basket cell P, pyramidal cell Com, commissural fibres Sch, Schaffer collaterals PP, perforant path. Excitatory synapses (o), inhibitory synapses ( ).

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