标题： 按螺旋和环精确枚举RNA二级结构 显示英文标题

标题： Exact enumeration of RNA secondary structures by helices and loops

摘要： 列举性研究RNA二级结构始于四十年前，由Waterman和他的同事开始。 自那时以来，RNA二级结构根据许多不同的结构特征进行了探索，例如，由Hofacker、Schuster和Stadler研究的螺旋、组分和环，由Nebel研究的顺序，由Clote研究的饱和结构，由Clote、Ponty和Stadler研究的$5^{\prime}$-$3^{\prime}$端距离，以及由Li和Reidys研究的彩虹谱。 然而，大多数贡献都是渐近结果，而推导显式公式则更为困难。 在本文中，我们得到了计数具有给定螺旋数量以及螺旋和环联合大小分布的RNA二级结构的精确公式，而一些与Hofacker、Schuster和Stadler相关的渐近结果已知约二十年了。 我们的方法是组合性的，分析了第一作者发现的RNA二级结构和平面树之间的最近双射，并提出了Chen的通过简单树森林计数树的双射方法的一种变体。 显示英文摘要

摘要： Enumerative studies of RNA secondary structures were initiated four decades ago by Waterman and his coworkers. Since then, RNA secondary structures have been explored according to many different structural characteristics, for instance, helices, components and loops by Hofacker, Schuster and Stadler, orders by Nebel, saturated structures by Clote, the $5^{\prime}$-$3^{\prime}$ end distance by Clote, Ponty and Steyaert, and the rainbow spectrum by Li and Reidys. However, the majority of the contributions are asymptotic results, and it is harder to derive explicit formulas. In this paper, we obtain exact formulas counting RNA secondary structures with a given number of helices as well as a given joint size distribution of helices and loops, while some related asymptotic results due to Hofacker, Schuster and Stadler have been known for about twenty years. Our approach is combinatorial, analyzing a recent bijection between RNA secondary structures and plane trees discovered by the first author and proposing a variation of Chen's bijective approach of counting trees by forests of simple trees.