A combinatorial enumeration problem of RNA secondary structures

Abstract

The total number of the RNA secondary structures with a limited length m in each hairpin loop, that is, S_m(n) has already been studied. In this paper, the number of this kind of RNA secondary structures is discussed with the technique of combinatorics. As a result, the recurrence relations, generating functions, explicit expressions, and some other properties were obtained. Furthermore, a new method to compute S_m (n)  is given in the end.

Key words: Combinatorial enumeration, generating function, RNA secondary structure.