A linear chain of nucleotides forms the primary structure of an RNA molecule. If two complementary nucleotides of this chain are in a stereochemically favorable position then they are joined by means of a hydrogen bound such that the linear molecule is folded into a three-dimensional conformation. This three-dimensional structure is of high interest since it determines the functionality of several kinds of RNA molecules. However, in order to reduce the complexity with respect to computational but also mathematical purposes, one usually considers only planar configurations - the so-called secondary structures of molecules - by restricting the possible hydrogen bounds. Recently, the speaker has studied the two major models for secondary structures, i.e. the combinatorial model and the Bernoulli-model, and compared the observed expected shape of a molecule to real existing structures. Under this viewpoint both models proved to be rather unrealistic [Neb02]. In this talk it will be shown how to find generating functions which allow to determine averages related to the shape of secondary structures such that the computed expected shape fits nicely to the real world data. The corresponding ideas can also be applied to other combinatorial structures and will be introduced using the example of tries in the unbiased Bernoulli-model.
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