嵌套相似类集合与 L & P 匹配之间的一一对应
A bijection between the set of nesting-similarity classes and L & P matchings
AI总结：
本文针对 L & P 匹配与嵌套相似类集合，构建了一个保持非交叉性和边端点序列的一一对应，从而建立了两个集合之间的双射关系。
摘要：
匹配经常被用来模拟 RNA 二级结构；然而，并非所有匹配都能实现为 RNA 基序。被称为 L $\&$ P 匹配的一类匹配，是最大发夹家族（LHF）中 RNA 二级结构最具限制性的模型。L $\&$ P 匹配在 2015 年由 Jefferson 枚举，并且它们与由 Klazar 枚举的匹配嵌套相似类集合具有相同的计数。我们提供了这两个集合之间的一一对应。该对应保持非交叉匹配，并保持从左到右读取每条边在该顶点是开始还是结束所得到的序列。
英文摘要：
Matchings are frequently used to model RNA secondary structures; however, not all matchings can be realized as RNA motifs. One class of matchings, called the L $\&$ P matchings, is the most restrictive model for RNA secondary structures in the Largest Hairpin Family (LHF). The L $\&$ P matchings were enumerated in $2015$ by Jefferson, and they are equinumerous with the set of nesting-similarity classes of matchings, enumerated by Klazar. We provide a bijection between these two sets. This bijection preserves noncrossing matchings, and preserves the sequence obtained reading left to right of whether an edge begins or ends at that vertex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
