2013/11/04 by Benjamin Mingming Fu, Fu, Benjamin Mingming, Christian M. Reidys +1
Biochemistry, Genetics and Molecular Biology · #Combinatorics (math.CO) #FOS: Mathematics #RNA Research and Splicing #RNA and protein synthesis mechanisms #RNA modifications and cancer
paper · pdf · doi:10.48550/arxiv.1311.0682
openalex publication_date 2013/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we compute the bivariate generating function of γ-matchings over two backbones, filtered by the number of arcs and the topological genus. γ-matchings over two backbones are chord-diagrams, obtained via concatenation and nesting of irreducible shapes of topological genus ≤ γ. We show that the key information is contained in the polynomials counting these shapes and provide recursions that allow to compute the latter. In particular we give a bijection between such irreducible shapes over one and two backbones. We present two applications of our results. The first is concerned with RNA-RNA interaction structures, obtained from the γ-matchings via symbolic methods. We secondly show that, using analytic-combinatorial methods, the topological genus satisfies a central limit theorem.