The Comparison Of DNA Sequences And The Enumeration Of RNA Secondary Structures

Comparison and analysis of biological sequences is one of the most important and basic problems of biological information. In this thesis, we make some studies and discussions for the comparison and analysis of sequences from the combinatorial point of view.In the first chapter, we introduce two methods of sequences comparison, one is the alignment, and the other is the method of the matrix invariant.In the second chapter, we introduce the existing graphical representations and present a new class of 2D graphical representations with a series of parameters. Two properties of the representation are given. Then we can know that the representation can avoid the degeneracy. We also give two generalized forms of our representation and prove that there is no circuit in the generalized forms. To these parameters we can assign various values according to the problem considered. And when parameters are assigned some special values, some graphical representations are the special cases of our graphical representation.In the last chapter, we consider the enumeration problem of RNA secondary structures only for the fixed pairs using the pairing function.