On Some Properties of Catalan Numbers and Application in RNA Secondary Structure.

Abstract

The purpose of this thesis is to understand the connections between the Catalan Numbers and Ribonucleic Acids (RNA) Secondary Structure. We show in this thesis the mathematical wealth of the Catalan numbers from several mathematical branches to one particular application in secondary structure of RNA used in protein folding. The di erent ways codes folding of RNA are represented. In particular, we show di erent representations of the Catalan numbers from the aspect of traditional combinatorial counting and generating functions as well as from classical function theory through orthogonal polynomial system where linear algebra plays role in computation. v