Enumeration of chord diagrams via topological recursion and quantum curve techniques

Autor:	Andersen, Jørgen Ellegaard, Fuji, Hiroyuki, Manabe, Masahide, Penner, Robert C., Sułkowski, Piotr
Rok vydání:	2016
Předmět:	Mathematical Physics High Energy Physics - Theory Mathematics - Combinatorics Quantitative Biology - Quantitative Methods
Zdroj:	Trav. Math. 25 (2017) 285
Druh dokumentu:	Working Paper
Popis:	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. Comment: 31 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.05839 Zobrazit plný text záznamu View this record from Arxiv