Title: An infinite class of unsaturated rooted trees corresponding to designable RNA secondary structures,
Abstract: An RNA secondary structure is designable if there is an RNA sequence which
can attain its maximum number of base pairs only by adopting that structure.
The combinatorial RNA design problem, introduced by Haleš et al. in 2016,
is to determine whether or not a given RNA secondary structure is designable.
Haleš et al. identified certain classes of designable and non-designable
secondary structures by reference to their corresponding rooted trees. We
introduce an infinite class of rooted trees containing unpaired nucleotides at
the greatest height, and prove constructively that their corresponding
secondary structures are designable. This complements previous results for the
combinatorial RNA design problem.