  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.
