The topological filtration of $γ$-structures

In this paper we study $γ$-structures filtered by topological genus. $γ$-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 $γ$-structure is composed by specific building blocks, that have topological genus less than or equal to $γ$, where composition means concatenation and nesting of such blocks. Our main results are the derivation of a new bivariate generating function for $γ$-structures via symbolic methods, the singularity analysis of the solutions and a central limit theorem for the distribution of topological genus in $γ$-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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