A bijection between the set of nesting-similarity classes and L & P matchings

Matchings are frequently used to model RNA secondary structures; however, notall matchings can be realized as RNA motifs. One class of matchings, called theL && P matchings, is the most restrictive model for RNA secondary structuresin the Largest Hairpin Family (LHF). The L && P matchings were enumerated in20152015 by Jefferson, and they are equinumerous with the set ofnesting-similarity classes of matchings, enumerated by Klazar. We provide abijection between these two sets. This bijection preserves noncrossingmatchings, and preserves the sequence obtained reading left to right of whetheran edge begins or ends at that vertex.