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arXiv · 1612.05839

Enumeration of chord diagrams via topological recursion and quantum curve techniques

Jørgen Ellegaard Andersen·Hiroyuki Fuji·Masahide Manabe·Robert C. Penner·Piotr Sułkowski
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Abstract

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 $β$-deformed Gaussian and RNA matrix models. We evaluate these expectation values by means of the $β$-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.

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Jørgen Ellegaard Andersen, Hiroyuki Fuji, Masahide Manabe, Robert C. Penner, Piotr Sułkowski. 2017-04-01. Enumeration of chord diagrams via topological recursion and quantum curve techniques. https://arxiv.org/abs/1612.05839

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