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arXiv · 1202.1061

The topological filtration of $\gamma$-structures

Thomas J. X. Li·Christian M. Reidys
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Abstract

In this paper we study $\gamma$-structures filtered by topological genus. $\gamma$-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A $\gamma$-structure is composed by specific building blocks, that have topological genus less than or equal to $\gamma$, where composition means concatenation and nesting of such blocks. Our main results are the derivation of a new bivariate generating function for $\gamma$-structures via symbolic methods, the singularity analysis of the solutions and a central limit theorem for the distribution of topological genus in $\gamma$-structures of given length. In our derivation specific bivariate polynomials play a central role. Their coefficients count particular motifs of fixed topological genus and they are of relevance in the context of genus recursion and novel folding algorithms.

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Thomas J. X. Li, Christian M. Reidys. 2012-02-06. The topological filtration of $\gamma$-structures. https://arxiv.org/abs/1202.1061

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