RNA Secondary Structure: New Combinatorial Representations and Statistics

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Jennifer Galovich, Mathematics


In this paper, we seek to construct new combinatorial representations of RNA secondary structure and investigate their properties. We will start by investigating models that are similar to existing models and easy to construct. The behavior of the combinatorial statistics on these models can easily be understood in terms of RNA secondary structure. We will then construct a permutation representation using one of these models as a basis. Since permutations are well understood in a variety of mathematics, we hope this model will encourage additional mathematical research on this topic. Finally, we explicitly identify the connections between the most common combinatorial statistics on these models and structural aspects of the RNA secondary structures they represent. These statistics help identify what structural phenomena are common in RNA secondary structure and what ones are not.

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