Work

Combinatorics of Loop Equations for Branched Covers of Sphere

Year: 2017

Type: article

Abstract: We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d’enfant. Furthermore, we give a proof of the quantum spectral curve equation for this problem. Then we consider the generalized case of four-colored maps and outline the idea of the proof of the corresponding spectral curve topological recursion.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnx047

Authors: Petr Dunin-Barkowski, Nicolas Orantin, Aleksandr Popolitov, Sergey Shadrin

Institutions: National Research University Higher School of Economics, Institute for Theoretical and Experimental Physics, École Polytechnique Fédérale de Lausanne, University of Amsterdam

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Russian Foundation for Basic Research, Nederlandse Organisatie voor Wetenschappelijk Onderzoek