A Remark on Deriving Precise Upper Bounds of the Number of the RNA Secondary Structures

TL;DR

This paper presents an elementary method for deriving precise upper bounds on the number of RNA secondary structures, applicable even when generating functions have multiple singularities and non-positive coefficients.

Contribution

It introduces a simple, undergraduate-level derivation technique for upper bounds that does not require positivity of Taylor coefficients or a single singularity.

Findings

Applicable to generating functions with multiple singularities

Does not require positivity of coefficients

Includes examples from current research literature

Abstract

An elementary, at the undergraduate level derivation is given of precise upper bounds of the number of various RNA secondary structures. The method works when the generating function has multiple singularities at the circle of convergence, nor does the method require the Taylor coefficients to be positive. Examples from the current research literature are considered.