论文标题
Zhang-Zhang丝带的多项式
Zhang-Zhang Polynomials of Ribbons
论文作者
论文摘要
我们报告了Zhang-Zhang多项式（又称ZZ多项式或CLAR覆盖多项式）的封闭式公式，该公式是一类重要类的基本可抑制苯苯二酚$ rb \ left（n_ {1}，n_ {1}，n_ {2}，n_ {2}，m_ {1}，m_ {1}，m_ {1}，m_ {1}，m_ {2} corrb，直接的推导基于最近开发的苯苯甲酸界面理论[Langner and Witek，Match Commun。数学。计算。化学84，143--176（2020）]。发现的公式为$ rb \ left（n_ {1}，n_ {2}，m_ {1}，m_ {1}，m_ {2} \ right）$的各种拓扑不变的表达式提供紧凑的表达：kekulé结构的数量，clar封面的数量，clar封面的数量，clar的数量，其CLAR数量和CLAR结构。最后两类的基本苯苯甲酸酯为封闭形式的Zz多项式公式有待发现的六角形薄片$ o \ left（k，m，n \右）$，并扁平矩形$或\ weft（m，n \ right）$。
We report a closed-form formula for the Zhang-Zhang polynomial (aka ZZ polynomial or Clar covering polynomial) of an important class of elementary pericondensed benzenoids $Rb\left(n_{1},n_{2},m_{1},m_{2}\right)$ usually referred to as ribbons. A straightforward derivation is based on the recently developed interface theory of benzenoids [Langner and Witek, MATCH Commun. Math. Comput. Chem. 84, 143--176 (2020)]. The discovered formula provides compact expressions for various topological invariants of $Rb\left(n_{1},n_{2},m_{1},m_{2}\right)$: the number of Kekulé structures, the number of Clar covers, its Clar number, and the number of Clar structures. The last two classes of elementary benzenoids, for which closed-form ZZ polynomial formulas remain to be found, are hexagonal flakes $O\left(k,m,n\right)$ and oblate rectangles $Or\left(m,n\right)$.
