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 matchingsArticle

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: October 23, 2017
    Submitted on: April 28, 2017
    Keywords: Mathematics - Combinatorics,05A19, 05C30

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