Enumeration of chord diagrams via topological recursion and quantum   curve techniques
  In this paper we consider the enumeration of orientable and non-orientable chord diagrams. We show that this enumeration is encoded in appropriate expectation values of the $\beta$-deformed Gaussian and RNA matrix models. We evaluate these expectation values by means of the $\beta$-deformed topological recursion, and - independently - using properties of quantum curves. We show that both these methods provide efficient and systematic algorithms for counting of chord diagrams with a given genus, number of backbones and number of chords. 
J{\o}rgen Ellegaard Andersen, Hiroyuki Fuji, Masahide Manabe, Robert   C. Penner, Piotr Su{\l}kowski
math-ph hep-th math.CO math.MP q-bio.QM