We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekulean benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons Rb, parallelograms M, vertically overlapping parallelograms MvM, horizontally overlapping parallelograms MhM, and intersecting parallelograms MxM. All formulas have the form of multiple sums over binomial coefficients. Three of the formulas are given with a proof based on the interface theory of benzenoids, while the remaining two formulas are presented as conjectures verified via extensive numerical tests. Both of the conjectured formulas have the form of a 2×2 determinant bearing close structural resemblance to analogous formulas for the number of Kekule structures derived from the John-Sachs theory of Kekule structures.

中文翻译：

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重叠苯类的透明覆盖：两个相同取向的平行四边形的情况

我们提出了五类复合Kekulean苯类的ZZ多项式的完整闭式公式，可以通过重叠两个平行四边形获得：广义带状Rb，平行四边形M，垂直重叠平行四边形MvM，水平重叠平行四边形MhM和相交平行四边形MxM。所有公式都具有二项式系数的多重和的形式。其中三个公式给出了基于苯类界面理论的证明，而其余两个公式则是通过大量数值试验验证的猜想。两个推测公式都具有 2×2 行列式的形式，其结构与源自凯库勒结构的约翰-萨克斯理论的凯库勒结构数的类似公式具有密切的结构相似性。