  In this paper, we study the combinatorial set of RNA secondary structures of
length $n$ with $m$ base-pairs. For a compact representation, we encode an RNA
secondary structure by the corresponding Motzkin word. For this combinatorial
set, we construct an AND/OR tree structure, find a bijection between the
combinatorial set and the set of variants of the AND/OR tree, and develop
algorithms for ranking and unranking the variants of the AND/OR tree. The
developed ranking and unranking algorithms have polynomial time complexity
$O(m^2 (n - m))$ for $m < n - 2 m$ and $O(m (n - m)^2)$ for $m > n - 2 m$. In
contrast to the existing algorithms, the new algorithms do not require
preprocessing steps and have better time complexity.
