## Megan A. Martinez ; Manda Riehl - A bijection between the set of nesting-similarity classes and L & P matchings

dmtcs:3291 - Discrete Mathematics & Theoretical Computer Science, January 22, 2018, Vol. 19 no. 2, Permutation Patterns 2016 - https://doi.org/10.23638/DMTCS-19-2-1
A bijection between the set of nesting-similarity classes and L & P matchings

Authors: Megan A. Martinez ; Manda Riehl

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.

Volume: Vol. 19 no. 2, Permutation Patterns 2016
Section: Permutation Patterns
Published on: January 22, 2018
Accepted on: January 22, 2018
Submitted on: April 28, 2017
Keywords: Mathematics - Combinatorics,05A19, 05C30