Enumeration of RNA Secondary Structures by Complexity

Many investigations in studying primary and secondary structures in Biology require theoretical statistical (that is enumerative) work. We solve one of these problems: enumerate secondary structures of single-stranded nucleic acids (RNA, tRNA, etc…) having a given complexity. This parameter has been introduced for energy computation purpose in order to predict the most stable secondary structure. The method relies on the (non-classical) use of non-commutative variables. Some orthogonal polynomials appear. The final solution shows a relationship between the parameter complexity and another parameter appearing in Hydrography and Botanic.